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Pre-Algebra : One-Step Equations with Decimals

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #1 : One Step Equations With Decimals

Solve for $\displaystyle x$:

0.75x=9 $\displaystyle 0.75x=9$

Possible Answers:

$\displaystyle 12$

$\displaystyle 21$

9.75 $\displaystyle 9.75$

$\displaystyle 6$

Correct answer:

$\displaystyle 12$

Explanation:

The goal is to isolate the variable on one side.

0.75x=9 $\displaystyle 0.75x=9$

Divide each side by 0.75 $\displaystyle 0.75$:

$\frac{0.75x}{0.75}=\frac{9}{0.75 }$ $\displaystyle \frac{0.75x}{0.75}=\frac{9}{0.75 }$

x=12 $\displaystyle x=12$

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Example Question #2 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\displaystyle 9.25x=74$

Possible Answers:

$\displaystyle -4$

$\displaystyle 8$

$\displaystyle -8$

$\displaystyle 4$

Correct answer:

$\displaystyle 8$

Explanation:

The goal is to isolate the variable on one side.

$\displaystyle 9.25x=74$

Divide each side by 9.25 $\displaystyle 9.25$:

$\frac{9.25x}{9.25}=\frac{74}{9.25}$ $\displaystyle \frac{9.25x}{9.25}=\frac{74}{9.25}$

x=8 $\displaystyle x=8$

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Example Question #1 : One Step Equations With Decimals

Solve for $\displaystyle n$:
$\displaystyle 1.05+n=3.72$

Possible Answers:

n=4.77 $\displaystyle n=4.77$

n=3.54 $\displaystyle n=3.54$

n=3.91 $\displaystyle n=3.91$

n=2.67 $\displaystyle n=2.67$

Correct answer:

n=2.67 $\displaystyle n=2.67$

Explanation:

$\displaystyle 1.05+n=3.72$

$\displaystyle 1.05+n-1.05=3.72-1.05$

n=2.67 $\displaystyle n=2.67$

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Example Question #3 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\displaystyle 1.75+x=4.2$

Possible Answers:

x=2.4 $\displaystyle x=2.4$

x=5.95 $\displaystyle x=5.95$

x=2.45 $\displaystyle x=2.45$

x=7.35 $\displaystyle x=7.35$

Correct answer:

x=2.45 $\displaystyle x=2.45$

Explanation:

$\displaystyle 1.75+x=4.2$

Subtract 1.75 from both sides of the equation:

$\displaystyle 1.75+x-1.75=4.2-1.75$

x=2.45 $\displaystyle x=2.45$

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Example Question #3 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\small .6x=6$ $\displaystyle \small .6x=6$

Possible Answers:

$\small 36$ $\displaystyle \small 36$

$\small 8$ $\displaystyle \small 8$

$\small 3.6$ $\displaystyle \small 3.6$

$\small 1$ $\displaystyle \small 1$

$\small 10$ $\displaystyle \small 10$

Correct answer:

$\small 10$ $\displaystyle \small 10$

Explanation:

To isolate $\displaystyle x$, we must divide both sides by .6:

$\small \small \frac{.6x}{.6}=\frac{6}{.6}$ $\displaystyle \small \small \frac{.6x}{.6}=\frac{6}{.6}$

$\small 1x=10$ $\displaystyle \small 1x=10$

$\small x=10$ $\displaystyle \small x=10$

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Example Question #4 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\frac{x}{0.15} = 3$ $\displaystyle \frac{x}{0.15} = 3$

Possible Answers:

$\displaystyle 3$

0.30 $\displaystyle 0.30$

0.15 $\displaystyle 0.15$

0.45 $\displaystyle 0.45$

3.45 $\displaystyle 3.45$

Correct answer:

0.45 $\displaystyle 0.45$

Explanation:

The goal is to isolate the variable on one side.

$\frac{x}{0.15} = 3$ $\displaystyle \frac{x}{0.15} = 3$

The opposite operation of division is multiplication, therefore , multiply each side by 0.15:

$\frac{0.15x}{0.15} = 0.15\times 3$ $\displaystyle \frac{0.15x}{0.15} = 0.15\times 3$

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

$1\times x = 0.15 \times 3$ $\displaystyle 1\times x = 0.15 \times 3$

The identity law of multiplication takes effect and we get the solution as:

$\displaystyle x = 0.45$

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Example Question #2 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\displaystyle x - 0.23 = 7.12$

Possible Answers:

7.35 $\displaystyle 7.35$

6.89 $\displaystyle 6.89$

7.36 $\displaystyle 7.36$

8.35 $\displaystyle 8.35$

30.96 $\displaystyle 30.96$

Correct answer:

7.35 $\displaystyle 7.35$

Explanation:

The goal is to isolate the variable on one side.

$\displaystyle x - 0.23 = 7.12$

The opposite operation of subtraction is addition so add 0.23 to each side:

$\displaystyle x - 0.23 + 0.23 = 7.12 + 0.23$

Simplifying, we get the final solution:

$\displaystyle x = 7.35$

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Example Question #3 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\displaystyle x - 1.94 = 2.06$

Possible Answers:

0.12 $\displaystyle 0.12$

1.12 $\displaystyle 1.12$

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

The goal is to isolate the variable on one side.

$\displaystyle x - 1.94 = 2.06$

The opposite operation of subtraction is addition so add 1.94 to each side:

$\displaystyle x - 1.94 + 1.94 = 2.06 + 1.94$

Simplifying, we get the final solution:

x = 4 $\displaystyle x = 4$

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Example Question #1 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\displaystyle x + 0.001 = -3$

Possible Answers:

3.001 $\displaystyle 3.001$

2.999 $\displaystyle 2.999$

-3.01 $\displaystyle -3.01$

-2.999 $\displaystyle -2.999$

-3.001 $\displaystyle -3.001$

Correct answer:

-3.001 $\displaystyle -3.001$

Explanation:

The goal is to isolate the variable on one side.

$\displaystyle x + 0.001 = -3$

The opposite operation of addition is subtraction so subtract 0.001 from each side:

$\displaystyle x + 0.001 - 0.001 = -3 - 0.001$

Simplifying, we get the final solution:

$\displaystyle x = -3.001$

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Example Question #5 : One Step Equations With Decimals

Solve for $\displaystyle x$:

$\displaystyle x + 8.11 = 0.002$

Possible Answers:

8.18 $\displaystyle 8.18$

8.112 $\displaystyle 8.112$

8.108 $\displaystyle 8.108$

-8.18 $\displaystyle -8.18$

-8.108 $\displaystyle -8.108$

Correct answer:

-8.108 $\displaystyle -8.108$

Explanation:

The goal is to isolate the variable on one side.

$\displaystyle x + 8.11 = 0.002$

The opposite operation of addition is subtraction so subtract 8.11 from each side:

$\displaystyle x + 8.11 - 8.11 = 0.002 - 8.11$

Simplifying, we get the final solution:

$\displaystyle x = -8.108$

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Pre-Algebra : One-Step Equations with Decimals

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : One Step Equations With Decimals

Example Question #2 : One Step Equations With Decimals

Example Question #1 : One Step Equations With Decimals

Example Question #3 : One Step Equations With Decimals

Example Question #3 : One Step Equations With Decimals

Example Question #4 : One Step Equations With Decimals

Example Question #2 : One Step Equations With Decimals

Example Question #3 : One Step Equations With Decimals

Example Question #1 : One Step Equations With Decimals

Example Question #5 : One Step Equations With Decimals

All Pre-Algebra Resources

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