Pre-Algebra Examples

$| 4 (x - 1) + 6 | = 10$

Step 1

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

$4 (x - 1) + 6 = \pm 10$

Step 2

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

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Step 2.1

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

$4 (x - 1) + 6 = 10$

Step 2.2

Simplify $4 (x - 1) + 6$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Apply the distributive property.

$4 x + 4 \cdot - 1 + 6 = 10$

Step 2.2.1.2

Multiply $4$ by $- 1$ .

$4 x - 4 + 6 = 10$

Step 2.2.2

Add $- 4$ and $6$ .

$4 x + 2 = 10$

Step 2.3

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

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Step 2.3.1

Subtract $2$ from both sides of the equation.

$4 x = 10 - 2$

Step 2.3.2

Subtract $2$ from $10$ .

$4 x = 8$

Step 2.4

Divide each term in $4 x = 8$ by $4$ and simplify.

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Step 2.4.1

Divide each term in $4 x = 8$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $4$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{4}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $8$ by $4$ .

$x = 2$

Step 2.5

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

$4 (x - 1) + 6 = - 10$

Step 2.6

Simplify $4 (x - 1) + 6$ .

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Step 2.6.1

Simplify each term.

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Step 2.6.1.1

Apply the distributive property.

$4 x + 4 \cdot - 1 + 6 = - 10$

Step 2.6.1.2

Multiply $4$ by $- 1$ .

$4 x - 4 + 6 = - 10$

Step 2.6.2

Add $- 4$ and $6$ .

$4 x + 2 = - 10$

Step 2.7

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

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Step 2.7.1

Subtract $2$ from both sides of the equation.

$4 x = - 10 - 2$

Step 2.7.2

Subtract $2$ from $- 10$ .

$4 x = - 12$

Step 2.8

Divide each term in $4 x = - 12$ by $4$ and simplify.

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Step 2.8.1

Divide each term in $4 x = - 12$ by $4$ .

$\frac{4 x}{4} = \frac{- 12}{4}$

Step 2.8.2

Simplify the left side.

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Step 2.8.2.1

Cancel the common factor of $4$ .

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Step 2.8.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 12}{4}$

Step 2.8.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{4}$

Step 2.8.3

Simplify the right side.

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Step 2.8.3.1

Divide $- 12$ by $4$ .

$x = - 3$

Step 2.9

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

$x = 2, - 3$