Algebra Examples

$| 5 x - 3 | - 6 = - 2 x + 12$

Step 1

Move all terms not containing $| 5 x - 3 |$ to the right side of the equation.

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Step 1.1

Add $6$ to both sides of the equation.

$| 5 x - 3 | = - 2 x + 12 + 6$

Step 1.2

Add $12$ and $6$ .

$| 5 x - 3 | = - 2 x + 18$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$5 x - 3 = \pm (- 2 x + 18)$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$5 x - 3 = - 2 x + 18$

Step 3.2

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

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Step 3.2.1

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

$5 x - 3 + 2 x = 18$

Step 3.2.2

Add $5 x$ and $2 x$ .

$7 x - 3 = 18$

Step 3.3

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

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Step 3.3.1

Add $3$ to both sides of the equation.

$7 x = 18 + 3$

Step 3.3.2

Add $18$ and $3$ .

$7 x = 21$

Step 3.4

Divide each term in $7 x = 21$ by $7$ and simplify.

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Step 3.4.1

Divide each term in $7 x = 21$ by $7$ .

$\frac{7 x}{7} = \frac{21}{7}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $7$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{21}{7}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{7}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $21$ by $7$ .

$x = 3$

Step 3.5

Next, use the negative value of the $\pm$ to find the second solution.

$5 x - 3 = - (- 2 x + 18)$

Step 3.6

Simplify $- (- 2 x + 18)$ .

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Step 3.6.1

Rewrite.

$5 x - 3 = 0 + 0 - (- 2 x + 18)$

Step 3.6.2

Simplify by adding zeros.

$5 x - 3 = - (- 2 x + 18)$

Step 3.6.3

Apply the distributive property.

$5 x - 3 = - (- 2 x) - 1 \cdot 18$

Step 3.6.4

Multiply.

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Step 3.6.4.1

Multiply $- 2$ by $- 1$ .

$5 x - 3 = 2 x - 1 \cdot 18$

Step 3.6.4.2

Multiply $- 1$ by $18$ .

$5 x - 3 = 2 x - 18$

Step 3.7

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

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Step 3.7.1

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

$5 x - 3 - 2 x = - 18$

Step 3.7.2

Subtract $2 x$ from $5 x$ .

$3 x - 3 = - 18$

Step 3.8

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

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Step 3.8.1

Add $3$ to both sides of the equation.

$3 x = - 18 + 3$

Step 3.8.2

Add $- 18$ and $3$ .

$3 x = - 15$

Step 3.9

Divide each term in $3 x = - 15$ by $3$ and simplify.

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Step 3.9.1

Divide each term in $3 x = - 15$ by $3$ .

$\frac{3 x}{3} = \frac{- 15}{3}$

Step 3.9.2

Simplify the left side.

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Step 3.9.2.1

Cancel the common factor of $3$ .

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Step 3.9.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 15}{3}$

Step 3.9.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 15}{3}$

Step 3.9.3

Simplify the right side.

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Step 3.9.3.1

Divide $- 15$ by $3$ .

$x = - 5$

Step 3.10

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 5$