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Pre-Algebra : Two-Step Equations with Integers

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Example Questions

Example Question #92 : Algebraic Equations

Solve for $\displaystyle q$:

$q ^{2}+ 116 = 165$ $\displaystyle q ^{2}+ 116 = 165$

Possible Answers:

$\pm$ $\displaystyle \pm$ $\displaystyle 8$

116 $\displaystyle 116$

281 $\displaystyle 281$

$\displaystyle 7$

$\pm$ $\displaystyle \pm$ $\displaystyle 7$

Correct answer:

$\pm$ $\displaystyle \pm$ $\displaystyle 7$

Explanation:

$q ^{2}+ 116 = 165$ $\displaystyle q ^{2}+ 116 = 165$

Subtract 116 $\displaystyle 116$ from both sides

^{$\displaystyle q ^{2}$ $\displaystyle = 49$}

Find the square root of $\displaystyle 49$

$\displaystyle q$ $= \pm7$ $\displaystyle = \pm7$

Remember that a negative number squared returns a positive so there are $\displaystyle 2$ possible solutions

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Example Question #41 : Two Step Equations With Integers

$\displaystyle 6t=18-3t$

Solve for $\displaystyle t$.

Possible Answers:

$\displaystyle -1$

$\displaystyle 3$

$\displaystyle 1$

$\displaystyle -2$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

Add 3t to both sides to get the variable on one side of the equation. Then divide each side by 18 to get the answer.

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Example Question #42 : Two Step Equations With Integers

$\displaystyle 72x+24=240$

Solve for $\displaystyle x$.

Possible Answers:

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 12$

$\displaystyle 3$

$\displaystyle 2$

Correct answer:

$\displaystyle 3$

Explanation:

Subtract 24 from each side to isolate the variable. Then divide each side by 72 to get x=3

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Example Question #43 : Two Step Equations With Integers

$\displaystyle -39g+7=-18g$

Solve for $\displaystyle g$.

Possible Answers:

$\displaystyle -3$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 39$

$\displaystyle -1$

$\displaystyle 18$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Add 39g to each side to isolate the variable coefficient. Then divide each side by 21 to get $g=\frac{1}{3}$ $\displaystyle g=\frac{1}{3}$.

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Example Question #44 : Two Step Equations With Integers

Find the value of $\displaystyle x$.

$\displaystyle 16x + 4 = 148$

Possible Answers:

$\displaystyle 64$

$\displaystyle 8$

$\displaystyle 12$

$\displaystyle 9$

$\displaystyle 20$

Correct answer:

$\displaystyle 9$

Explanation:

$\displaystyle 16x + 4 = 148$

- 4 -4

$\displaystyle 16x = 144$

/16 /16

x = 9 $\displaystyle x = 9$

Check your answer by substituting the value of X back into the equation. When solved both sides of the equation should be equal.

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Example Question #45 : Two Step Equations With Integers

Solve for $\displaystyle t$:

$\displaystyle 16t+2=66$

Possible Answers:

t=4 $\displaystyle t=4$

t=5 $\displaystyle t=5$

t=4.75 $\displaystyle t=4.75$

t=4.25 $\displaystyle t=4.25$

t=6 $\displaystyle t=6$

Correct answer:

t=4 $\displaystyle t=4$

Explanation:

Solve for t in two steps. First move all constants to the opposite side. Then move constants attached to the variable you are solving for to the opposite side.

$\displaystyle 16t+2=66$

Subtract 2 from both sides:

$16t{\color{Red} +2-2}=66-2$ $\displaystyle 16t{\color{Red} +2-2}=66-2$

The red terms cancel and the right side is subtracted as usual.

16t=64 $\displaystyle 16t=64$

Divide both sides by 16:

$\frac{{\color{Red} 16}t}{{\color{Red} 16}}=\frac{64}{16}$ $\displaystyle \frac{{\color{Red} 16}t}{{\color{Red} 16}}=\frac{64}{16}$

The red terms cancel and the right side is divided as usual.

t=4 $\displaystyle t=4$

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Example Question #46 : Two Step Equations With Integers

Solve: $\displaystyle 4x -2 = 2$

Possible Answers:

$\displaystyle -1$

$\displaystyle 0$

$\displaystyle 1$

$\displaystyle 4$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Correct answer:

$\displaystyle 1$

Explanation:

Add two on both sides of the equation.

$\displaystyle 4x -2+2 = 2+2$

4x=4 $\displaystyle 4x=4$

Divide by four on both sides.

$\frac{4x}{4}=\frac{4}{4}$ $\displaystyle \frac{4x}{4}=\frac{4}{4}$

x=1 $\displaystyle x=1$

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Example Question #47 : Two Step Equations With Integers

Solve: $\displaystyle -3x + 3 = -3$

Possible Answers:

$\displaystyle 1$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 0$

$\displaystyle -1$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate the unknown variable, first subtract three from both sides.

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

-3x=-6 $\displaystyle -3x=-6$

Divide by negative three on both sides.

$\frac{-3}{-3}x=\frac{-6}{-3}$ $\displaystyle \frac{-3}{-3}x=\frac{-6}{-3}$

x=2 $\displaystyle x=2$

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Example Question #44 : Two Step Equations With Integers

Solve: $\displaystyle 7x-7 = 18$

Possible Answers:

$\frac{7}{9}$ $\displaystyle \frac{7}{9}$

$\frac{25}{7}$ $\displaystyle \frac{25}{7}$

$\frac{7}{18}$ $\displaystyle \frac{7}{18}$

$\frac{18}{7}$ $\displaystyle \frac{18}{7}$

$\frac{11}{7}$ $\displaystyle \frac{11}{7}$

Correct answer:

$\frac{25}{7}$ $\displaystyle \frac{25}{7}$

Explanation:

Add seven on both sides of the equation.

$\displaystyle 7x-7+7 = 18+7$

7x=25 $\displaystyle 7x=25$

Divide by seven on both sides.

$x=\frac{25}{7}$ $\displaystyle x=\frac{25}{7}$

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Example Question #49 : Two Step Equations With Integers

Solve: $\displaystyle 6x+12 = -96$

Possible Answers:

$\displaystyle -18$

$\displaystyle 24$

$\displaystyle -24$

$\displaystyle 14$

$\displaystyle 18$

Correct answer:

$\displaystyle -18$

Explanation:

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Subtract 12 from both sides of the equation.

$\displaystyle 6x+12 -12= -96-12$

$\displaystyle 6x= -108$

Divide by six on both sides of the equation.

$\frac{6x}{6}= \frac{-108}{6}$ $\displaystyle \frac{6x}{6}= \frac{-108}{6}$

x=-18 $\displaystyle x=-18$

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Pre-Algebra : Two-Step Equations with Integers

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #92 : Algebraic Equations

Example Question #41 : Two Step Equations With Integers

Example Question #42 : Two Step Equations With Integers

Example Question #43 : Two Step Equations With Integers

Example Question #44 : Two Step Equations With Integers

Example Question #45 : Two Step Equations With Integers

Example Question #46 : Two Step Equations With Integers

Example Question #47 : Two Step Equations With Integers

Example Question #44 : Two Step Equations With Integers

Example Question #49 : Two Step Equations With Integers

All Pre-Algebra Resources

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