Pre-Algebra Examples

$| 2 x - 5 | = | 9 x + 7 |$

Step 1

Rewrite the equation as $| 9 x + 7 | = | 2 x - 5 |$ .

$| 9 x + 7 | = | 2 x - 5 |$

Step 2

Rewrite the absolute value equation as four equations without absolute value bars.

$9 x + 7 = 2 x - 5$

$9 x + 7 = - (2 x - 5)$

$- (9 x + 7) = 2 x - 5$

$- (9 x + 7) = - (2 x - 5)$

Step 3

After simplifying, there are only two unique equations to be solved.

$9 x + 7 = 2 x - 5$

$9 x + 7 = - (2 x - 5)$

Step 4

Solve $9 x + 7 = 2 x - 5$ for $x$ .

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $2 x$ from both sides of the equation.

$9 x + 7 - 2 x = - 5$

Step 4.1.2

Subtract $2 x$ from $9 x$ .

$7 x + 7 = - 5$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Subtract $7$ from both sides of the equation.

$7 x = - 5 - 7$

Step 4.2.2

Subtract $7$ from $- 5$ .

$7 x = - 12$

Step 4.3

Divide each term in $7 x = - 12$ by $7$ and simplify.

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Step 4.3.1

Divide each term in $7 x = - 12$ by $7$ .

$\frac{7 x}{7} = \frac{- 12}{7}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $7$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 12}{7}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{7}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$x = - \frac{12}{7}$

Step 5

Solve $9 x + 7 = - (2 x - 5)$ for $x$ .

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Step 5.1

Simplify $- (2 x - 5)$ .

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Step 5.1.1

Rewrite.

$9 x + 7 = 0 + 0 - (2 x - 5)$

Step 5.1.2

Simplify by adding zeros.

$9 x + 7 = - (2 x - 5)$

Step 5.1.3

Apply the distributive property.

$9 x + 7 = - (2 x) - - 5$

Step 5.1.4

Multiply.

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Step 5.1.4.1

Multiply $2$ by $- 1$ .

$9 x + 7 = - 2 x - - 5$

Step 5.1.4.2

Multiply $- 1$ by $- 5$ .

$9 x + 7 = - 2 x + 5$

Step 5.2

Move all terms containing $x$ to the left side of the equation.

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Step 5.2.1

Add $2 x$ to both sides of the equation.

$9 x + 7 + 2 x = 5$

Step 5.2.2

Add $9 x$ and $2 x$ .

$11 x + 7 = 5$

Step 5.3

Move all terms not containing $x$ to the right side of the equation.

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Step 5.3.1

Subtract $7$ from both sides of the equation.

$11 x = 5 - 7$

Step 5.3.2

Subtract $7$ from $5$ .

$11 x = - 2$

Step 5.4

Divide each term in $11 x = - 2$ by $11$ and simplify.

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Step 5.4.1

Divide each term in $11 x = - 2$ by $11$ .

$\frac{11 x}{11} = \frac{- 2}{11}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $11$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 2}{11}$

Step 5.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{11}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Move the negative in front of the fraction.

$x = - \frac{2}{11}$

Step 6

List all of the solutions.

$x = - \frac{12}{7}, - \frac{2}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{7}, - \frac{2}{11}$

Decimal Form:

$x = - 1.\overline{714285}, - 0.\overline{18}$

Mixed Number Form:

$x = - 1 \frac{5}{7}, - \frac{2}{11}$