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Algebra II : Basic Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #181 : Solving Equations

Solve for $\displaystyle x$.

$\displaystyle 8(x+4)=6(x+1)$

Possible Answers:

$\displaystyle -12$

$\displaystyle -8$

$\displaystyle 10$

$\displaystyle 9$

$\displaystyle -13$

Correct answer:

$\displaystyle -13$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle 8(x+4)=6(x+1)$

Distribute the number to each term in the parentheses.

$\displaystyle 8x+32=6x+6$

Subtract $\displaystyle 6x$ and $\displaystyle 32$ on both sides.

2x=-26 $\displaystyle 2x=-26$

Divide $\displaystyle 2$ on both sides.

x=-13 $\displaystyle x=-13$

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Example Question #661 : Basic Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 9x-58=203$

Possible Answers:

$\displaystyle 27$

$\displaystyle 29$

$\displaystyle 35$

$\displaystyle 31$

$\displaystyle 33$

Correct answer:

$\displaystyle 29$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle 9x-58=203$

Add $\displaystyle 58$ on both sides.

9x=261 $\displaystyle 9x=261$

Divide $\displaystyle 9$ on both sides.

x=29 $\displaystyle x=29$

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Example Question #662 : Basic Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 7x-48=-405$

Possible Answers:

$\displaystyle -51$

$\displaystyle 48$

$\displaystyle -49$

$\displaystyle 53$

$\displaystyle 52$

Correct answer:

$\displaystyle -51$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle 7x-48=-405$

Add $\displaystyle 48$ on both sides.

7x=-357 $\displaystyle 7x=-357$

Divide $\displaystyle 7$ on both sides.

x=-51 $\displaystyle x=-51$

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Example Question #663 : Basic Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 3(x-3)=4(x-4)$

Possible Answers:

$\displaystyle 5$

$\displaystyle 7$

$\displaystyle 11$

$\displaystyle 6$

$\displaystyle 8$

Correct answer:

$\displaystyle 7$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle 3(x-3)=4(x-4)$

Distribute the number to each term in the parentheses.

$\displaystyle 3x-9=4x-16$

Subtract $\displaystyle 3x$ and add $\displaystyle 16$ on both sides.

x=7 $\displaystyle x=7$

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Example Question #664 : Basic Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 25x=1500$

Possible Answers:

$\displaystyle 64$

$\displaystyle 52$

$\displaystyle 60$

$\displaystyle 48$

$\displaystyle 70$

Correct answer:

$\displaystyle 60$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle 25x=1500$

Divide $\displaystyle 25$ on both sides.

x=60 $\displaystyle x=60$

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Example Question #185 : Solving Equations

Solve for $\displaystyle x$.

$\displaystyle 36x=-1368$

Possible Answers:

$\displaystyle -37$

$\displaystyle 40$

$\displaystyle 42$

$\displaystyle -39$

$\displaystyle -38$

Correct answer:

$\displaystyle -38$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle 36x=-1368$

Divide $\displaystyle 36$ on both sides.

x=-38 $\displaystyle x=-38$

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Example Question #186 : Solving Equations

Solve for $\displaystyle x$.

$\displaystyle -39x=-1599$

Possible Answers:

$\displaystyle 51$

$\displaystyle -41$

$\displaystyle 41$

$\displaystyle 46$

$\displaystyle -51$

Correct answer:

$\displaystyle 41$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\displaystyle -39x=-1599$

Divide $\displaystyle -39$ on both sides.

x=41 $\displaystyle x=41$

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Example Question #187 : Solving Equations

Solve for $\displaystyle x$.

$\frac{x}{7}=9.2$ $\displaystyle \frac{x}{7}=9.2$

Possible Answers:

72.3 $\displaystyle 72.3$

65.4 $\displaystyle 65.4$

63.4 $\displaystyle 63.4$

64.4 $\displaystyle 64.4$

68.6 $\displaystyle 68.6$

Correct answer:

64.4 $\displaystyle 64.4$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{x}{7}=9.2$ $\displaystyle \frac{x}{7}=9.2$

Multiply $\displaystyle 7$ on both sides.

x=64.4 $\displaystyle x=64.4$

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Example Question #187 : Solving Equations

Solve for $\displaystyle x$.

$\frac{-x}{13}=14.6$ $\displaystyle \frac{-x}{13}=14.6$

Possible Answers:

222.2 $\displaystyle 222.2$

-189.8 $\displaystyle -189.8$

-196.4 $\displaystyle -196.4$

-208.8 $\displaystyle -208.8$

214.8 $\displaystyle 214.8$

Correct answer:

-189.8 $\displaystyle -189.8$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{-x}{13}=14.6$ $\displaystyle \frac{-x}{13}=14.6$

Multiply $\displaystyle 13$ on both sides.

$\displaystyle -x=189.8$

Divide $\displaystyle -1$ on both sides.

$\displaystyle x=-189.8$

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Example Question #665 : Basic Single Variable Algebra

Solve for $\displaystyle x$.

$\frac{x}{-3.3}=-6.9$ $\displaystyle \frac{x}{-3.3}=-6.9$

Possible Answers:

-27.27 $\displaystyle -27.27$

55.21 $\displaystyle 55.21$

43.67 $\displaystyle 43.67$

22.77 $\displaystyle 22.77$

-37.57 $\displaystyle -37.57$

Correct answer:

22.77 $\displaystyle 22.77$

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{x}{-3.3}=-6.9$ $\displaystyle \frac{x}{-3.3}=-6.9$

Multiply -3.3 $\displaystyle -3.3$ on both sides.

$\displaystyle x=-22.77$

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Algebra II : Basic Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #181 : Solving Equations

Example Question #661 : Basic Single Variable Algebra

Example Question #662 : Basic Single Variable Algebra

Example Question #663 : Basic Single Variable Algebra

Example Question #664 : Basic Single Variable Algebra

Example Question #185 : Solving Equations

Example Question #186 : Solving Equations

Example Question #187 : Solving Equations

Example Question #187 : Solving Equations

Example Question #665 : Basic Single Variable Algebra

All Algebra II Resources

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