Starting at $$-18.5$$, Carlos moves distance $$12.75$$ in the positive direction: $$-18.5 + 12.75 = -5.75$$. Then he moves distance $$8.25$$ in the positive direction: $$-5.75 + 8.25 = 2.5$$. His final balance is $$+\2.50$$, meaning $$\2.50$$ credit. Choice B uses the wrong sign from calculation error. Choice C adds all amounts without considering the debt. Choice D gives the net deposit amount, not the final balance.

When you see a problem involving positive and negative changes to a starting value, you're working with integer addition on a number line. Think of moving right for positive changes and left for negative changes.

Start at the initial position of $$-\2.40$$ (which means $$\2.40$$ below the opening price). Now apply each change step by step:

First change: $$+\1.85$$. Moving right from $$-\2.40$$:

$$-\2.40 + \1.85 = -\0.55$$

Second change: $$-\0.95$$. Moving left from $$-\0.55$$:

$$-\0.55 + (-\0.95) = -\0.55 - \0.95 = -\1.50$$

Third change: $$+\0.75$$. Moving right from $$-\1.50$$:

$$-\1.50 + \0.75 = -\0.75$$

The final position is $$-\0.75$$, meaning $$\0.75$$ below the opening price.

Choice A ($$-\1.65$$) likely comes from adding the absolute values of all negative changes and subtracting positive ones incorrectly. Choice B ($$+\0.75$$) represents forgetting the negative sign in your final calculation. Choice D ($$+\1.65$$) suggests adding all the changes without considering their signs properly, then making the result positive.

Strategy tip: When working with signed numbers, keep track of your running total after each step rather than trying to do everything at once. Draw a simple number line if it helps you visualize the movements, and always double-check whether your final answer should be positive or negative.

When you encounter problems involving temperature changes or any sequence of positive and negative values, you're working with integer addition. Think of this as moving along a number line, where positive changes move you right and negative changes move you left.

Start with the initial temperature of $$-4.8°C$$ and apply each change in order. First, add $$+2.3°C$$: $$-4.8 + 2.3 = -2.5°C$$. Next, add $$-6.7°C$$ (which means subtracting): $$-2.5 + (-6.7) = -2.5 - 6.7 = -9.2°C$$. Finally, add $$+3.1°C$$: $$-9.2 + 3.1 = -6.1°C$$.

Looking at the wrong answers: Choice A ($$1.7°C$$) likely comes from ignoring negative signs and just working with absolute values. Choice B ($$-1.7°C$$) might result from calculation errors, perhaps forgetting to apply one of the changes correctly. Choice C ($$6.1°C$$) gives you the right numerical value but the wrong sign, suggesting you may have treated some negative changes as positive ones.

The correct answer is D: $$-6.1°C$$.

Remember to track your signs carefully in multi-step problems like this. A helpful strategy is to write out each step completely rather than trying to do it all in your head. When adding negative numbers, it's often clearer to rewrite them as subtraction: $$-2.5 + (-6.7)$$ becomes $$-2.5 - 6.7$$, which many students find easier to calculate accurately.

Starting at $$-120$$, the submarine moves distance $$|45| = 45$$ in the positive direction (toward surface): $$-120 + 45 = -75$$. Then it moves distance $$|{-30}| = 30$$ in the negative direction (deeper): $$-75 + (-30) = -105$$. The final depth is $$-105$$ feet. Choice B stops after the first move. Choice C gives the correct magnitude but incorrect sign. Choice D combines both errors from choices B and C.

When you see a problem involving changes to a starting value, you're working with integer addition. Think of this as tracking movements on a number line, where positive numbers move right (up) and negative numbers move left (down).

Start with the character's initial health: $$-15$$ points. Now apply each change in order. First, add the healing: $$-15 + 22 = +7$$ points. Next, subtract the damage: $$+7 + (-8) = +7 - 8 = -1$$ points. Finally, add the second healing: $$-1 + 4 = +3$$ points.

You can also solve this by combining all changes first: $$-15 + 22 - 8 + 4 = -15 + 18 = +3$$ points.

Looking at the wrong answers: Choice A ($$-3$$) likely comes from miscalculating the final step, perhaps doing $$-1 - 4$$ instead of $$-1 + 4$$. Choice C ($$+7$$) represents stopping after the first healing and forgetting about the remaining damage and healing. Choice D ($$-7$$) could result from sign errors, possibly calculating $$-15 - 22 + 8 + 4$$ by treating the first healing as damage.

The correct answer is B: $$+3$$ health points.

Remember that adding a negative number is the same as subtracting, and subtracting a negative is the same as adding. When tracking multiple changes to an initial value, work step-by-step and pay careful attention to whether each change is positive or negative. Double-check your signs at each step.

This question tests interpreting p + q on a number line: start at p=3, move distance |q|=|5|=5 units in the direction determined by the sign of q=5 (right if positive, left if negative), ending at p+q=8. Number line addition: locate starting position p=3 (can be positive, negative, or zero), identify distance to move |q|=5 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=8. For example, -3 + (-6) starts at -3, adding -6 moves left 6 units (negative addition moves left), ending at -9 (farther left/more negative); or 2+5 starts at 2, moves right 5, ends at 7; or -5+8 starts at -5, moves right 8, crosses zero to end at +3. The correct interpretation is starting at position 3, moving a distance of 5 units to the right (since 5 is positive), and ending at the final position of 8. A common error is choosing the wrong direction, like moving left for a positive addition (as in choice A, ending at -2), or starting at the wrong position like 0 instead of 3 (choice B), or moving the wrong distance like 3 units instead of 5 (choice D). The process is: (1) locate p=3 on the number line (mark starting position), (2) determine |q|=5 distance, (3) determine direction (q positive→right), (4) move from p right 5 units, (5) mark final position at 8 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); contexts reinforce: deposit (+) moves balance right (increases), withdrawal (-) moves left (decreases), temperature rise (+) moves right (warmer), fall (-) moves left (cooler).

This question tests interpreting p + q on a number line: start at p=7, move distance |q|=|-4|=4 units in the direction determined by the sign of q=-4 (right if positive, left if negative), ending at p+q=3. Number line addition: locate starting position p=7 (can be positive, negative, or zero), identify distance to move |q|=4 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=3. Example: 7+(-4) starts at 7 (p=7), moves left 4 units (q=-4, distance=4, direction=left), ends at 3 (7-4=3, or thinking: 7 is 4 more than 3, moving left 4 from 7 reaches 3); context: temperature -5°C rises 8° (adds +8): start -5, move right 8 units (positive rise), end at 3°C (-5+8=3). The correct interpretation is starting at position 7, moving a distance of 4 units to the left (since -4 is negative), and ending at the final position of 3. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice B, ending at 11), or starting at the wrong position like 0 instead of 7 (choice C), or treating distance as signed like moving '-4 units' to the left interpreted as right (choice D). The process is: (1) locate p=7 on the number line (mark starting position), (2) determine |q|=4 distance, (3) determine direction (q negative→left), (4) move from p left 4 units, (5) mark final position at 3 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); mistakes: direction from sign confused (most common error: thinking negative addition moves right), distance as signed quantity (using -4 as distance when should use 4).

This question tests interpreting p + q on a number line: start at p=1/2, move distance |q|=|-3/4|=3/4 units in the direction determined by the sign of q=-3/4 (right if positive, left if negative), ending at p+q=-1/4. Number line addition: locate starting position p=1/2 (can be positive, negative, or zero), identify distance to move |q|=3/4 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=-1/4. For example, -3 + (-6) starts at -3, adding -6 moves left 6 units (negative addition moves left), ending at -9 (farther left/more negative); or 2+5 starts at 2, moves right 5, ends at 7; or -5+8 starts at -5, moves right 8, crosses zero to end at +3. The correct interpretation is starting at position 1/2, moving a distance of 3/4 units to the left (since -3/4 is negative), and ending at the final position of -1/4. A common error is choosing the wrong direction, like moving right for a negative addition (as in choice A, ending at 5/4), or starting at the wrong position like -3/4 instead of 1/2 (choice B), or treating distance as signed like moving '-3/4 units' to the left interpreted as right (choice D). The process is: (1) locate p=1/2 on the number line (mark starting position), (2) determine |q|=3/4 distance, (3) determine direction (q negative→left), (4) move from p left 3/4 units, (5) mark final position at -1/4 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); mistakes: direction from sign confused (most common error: thinking negative addition moves right), distance as signed quantity (using -3/4 as distance when should use 3/4).

This question tests interpreting p + q on a number line: start at p=3, move distance |q|=|5|=5 units in the direction determined by the sign of q=5 (right if positive, left if negative), ending at p+q=8. Number line addition involves locating the starting position p=3 (positive, to the right of zero), identifying the distance to move |q|=5 (magnitude regardless of sign), determining the direction from the sign of q (positive, so move right toward larger numbers), and landing at 8. For example, like 7 + (-4) starts at 7, moves left 4 units, ends at 3; in a context, if temperature is -5°C and rises 8° (adds +8), start at -5, move right 8 units, end at 3°C. Another example: -3 + (-6) starts at -3, moves left 6 units, ends at -9; or 2 + 5 starts at 2, moves right 5, ends at 7; or -5 + 8 starts at -5, moves right 8, ends at 3. The correct interpretation is starting at 3, moving right 5 units (since 5 is positive), ending at 8, which matches choice C. A common error is moving in the wrong direction, like left for positive addition, or starting at the wrong position such as 0 or switching p and q. The process is: (1) locate p=3 on the number line, (2) determine |q|=5 distance, (3) determine direction (positive → right), (4) move right 5 from 3, (5) mark final position at 8; remember, adding positive increases the value (moves right), while adding negative decreases it (moves left).

This question tests interpreting p + q on a number line: start at p=2.5, move distance |q|=|-3.2|=3.2 units in the direction determined by the sign of q=-3.2 (right if positive, left if negative), ending at p+q=-0.7. Number line addition: locate starting position p=2.5 (can be positive, negative, or zero), identify distance to move |q|=3.2 (magnitude of q: |-4|=4 units, |5|=5 units regardless of sign), determine direction from sign of q (if q>0 move right toward larger numbers, if q<0 move left toward smaller), land at p+q=-0.7. For example, -3 + (-6) starts at -3, adding -6 moves left 6 units (negative addition moves left), ending at -9 (farther left/more negative); or 2+5 starts at 2, moves right 5, ends at 7; or -5+8 starts at -5, moves right 8, crosses zero to end at +3. The correct interpretation is starting at position 2.5, moving a distance of 3.2 units to the left (since going down is -3.2, negative), and ending at the final position of -0.7 meters. A common error is choosing the wrong direction, like moving right for a negative change (as in choice A, ending at 5.7), or moving the wrong distance like 1.8 units (choice C), or starting at the wrong position like 0 (choice D). The process is: (1) locate p=2.5 on the number line (mark starting position), (2) determine |q|=3.2 distance, (3) determine direction (q negative→left), (4) move from p left 3.2 units, (5) mark final position at -0.7 (p+q result). Sign rules: adding positive increases (moves right on number line to larger), adding negative decreases (moves left to smaller); contexts reinforce: elevation increase (+) moves right (higher), decrease (-) moves left (lower); mistakes: direction from sign confused.