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Pre-Algebra : Algebraic Equations

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Example Questions

Example Question #55 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve: -7+x = 2

Possible Answers:

$-\frac{7}{2}$

Correct answer:

Explanation:

Solve by adding seven on both sides of the equation. This will isolate on both sides of the equation.

-7+x +(7) = 2+(7)

Add the left side of the equation.

x=2+7

Add the right side of the equation.

x=9

The answer is .

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Example Question #53 : One Step Equations

Solve for :

$\frac{x}{4}=-9$

Possible Answers:

x=-13

x=36

x=-5

x=0

x=-36

Correct answer:

x=-36

Explanation:

To solve this equation, we must isolate on the left side by multiplying each side by , as follows:

$\frac{x}{4}=-9$

$4(\frac{x}{4})=(-9)(4)$

x=-36

Therefore, the correct answer is x=-36 .

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Example Question #52 : One Step Equations With Integers

Solve for x in the following equation.

x - 12 = 9

Possible Answers:

x = 3

x = 9

x = 19

x = 12

x = 21

Correct answer:

x = 21

Explanation:

When solving for x, we want x to be alone. Therefore, in the equation

x - 12 = 9

we add 12 to both sides.

x - 12 + 12 = 9 + 12

x = 21

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Example Question #57 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Solve:

x-241=241

Possible Answers:

482

241

Correct answer:

482

Explanation:

To solve for , we must isolate it to one side of the equation, as follows:

x-241=241

x-241+241=241+241

x=482

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Example Question #54 : One Step Equations

Find the solution for the variable m.

346 + m = 1111

Possible Answers:

m = 755

m = 764

m = 766

m = 765

m = 765.5

Correct answer:

m = 765

Explanation:

In order to find the solution we must isolate the variable m. The first step is to subtract 346 from both sides as follows:

346 - 346 + m = 1111 - 346

0 + m = 765

m = 765

We can check the answer by plugging in our solution of 765 into the original equation.

346 + 765 = 1111

1111 = 1111

It works.

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Example Question #231 : Expressions & Equations

Solve for : -7x=-35

Possible Answers:

$x=\frac{7}{35}$

x=-5

$x=-\frac{7}{35}$

x=5

Correct answer:

x=5

Explanation:

-7x=-35

$\frac{-7x}{-7}=\frac{-35}{-7}$

x=5

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Example Question #1 : One Step Equations With Fractions

Solve for :

$\frac{x}{\frac{2}{3}}=6$

Possible Answers:

Correct answer:

Explanation:

Isolate the variable to one side.

Multiply each side by $\frac{2}{3}$ :

$\frac{x}{\frac{2}{3}}=6$

$\frac{x\frac{2}{3}}{\frac{2}{3}}=\frac{6}{1}*\frac{2}{3}$

Simplify and reduce:

x=4

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Example Question #2 : One Step Equations With Fractions

Solve for :

$\frac{2}{5}x=8$

Possible Answers:

$3\frac{1}{5}$

$8\frac{2}{5}$

Correct answer:

Explanation:

Step 1: Multiply both sides of the equation by the fraction's reciprocal to get alone on one side:

$\frac{5}{2}*\frac{2}{5}x=8*\frac{5}{2}$

$1x=8*\frac{5}{2}$

$x=8*\frac{5}{2}$

Step 2: Multiply:

$x=8*\frac{5}{2}=\frac{40}{2}=20$

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Example Question #3 : One Step Equations With Fractions

Solve for :

$\frac{x}{\frac{4}{5}} = 2$

Possible Answers:

$\frac{10}{4}$

$\frac{8}{5}$

$\frac{5}{8}$

$\frac{8}{10}$

$\frac{4}{10}$

Correct answer:

$\frac{8}{5}$

Explanation:

The goal is to isolate the variable on one side.

$\frac{x}{\frac{4}{5}} = 2$

The opposite operation of division is multiplication, therefore , multiply each side by $\frac{4}{5}$ :

$\frac{\frac{4}{5}x}{\frac{4}{5}} = \frac{4}{5}\times 2$

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

$1\times x = \frac{4}{5} \times 2$

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

$x = \frac{8}{5}$

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Example Question #3 : One Step Equations With Fractions

Solve for :

$\frac{6}{7} x = 3$

Possible Answers:

$\frac{18}{7}$

$\frac{18}{21}$

$\frac{21}{18}$

$\frac{7}{2}$

$\frac{18}{6}$

Correct answer:

$\frac{7}{2}$

Explanation:

The goal is to isolate the variable on one side.

$\frac{6}{7} x = 3$

The opposite operation of multiplication is division, therefore, we can either divide each side by $\frac{6}{7}$ or multiply each side by its reciprocal $\frac{7}{6}$ :

$\frac{7}{6}\times \frac{6}{7}x = \frac{7}{6}\times 3$

The left hand side can be reduced by recalling that anything multiplying a fraction by its reciprocal is equal to 1:

$1\times x = \frac{7}{6} \times 3$

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

$x = \frac{21}{6}$

However, this solution can be reduced by dividing both the numerator and denominator by 3:

$x = \frac{7}{2}$

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Pre-Algebra : Algebraic Equations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #55 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #53 : One Step Equations

Example Question #52 : One Step Equations With Integers

Example Question #57 : Evaluate Expressions: Ccss.Math.Content.6.Ee.A.2c

Example Question #54 : One Step Equations

Example Question #231 : Expressions & Equations

Example Question #1 : One Step Equations With Fractions

Example Question #2 : One Step Equations With Fractions

Example Question #3 : One Step Equations With Fractions

Example Question #3 : One Step Equations With Fractions

All Pre-Algebra Resources

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