Algebra Examples

$3 - | 8 x - 6 | = 3$

Step 1

Move all terms not containing $| 8 x - 6 |$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$- | 8 x - 6 | = 3 - 3$

Step 1.2

Subtract $3$ from $3$ .

$- | 8 x - 6 | = 0$

Step 2

Divide each term in $- | 8 x - 6 | = 0$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- | 8 x - 6 | = 0$ by $- 1$ .

$\frac{- | 8 x - 6 |}{- 1} = \frac{0}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{| 8 x - 6 |}{1} = \frac{0}{- 1}$

Step 2.2.2

Divide $| 8 x - 6 |$ by $1$ .

$| 8 x - 6 | = \frac{0}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $- 1$ .

$| 8 x - 6 | = 0$

Step 3

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

$8 x - 6 = \pm 0$

Step 4

Plus or minus $0$ is $0$ .

$8 x - 6 = 0$

Step 5

Add $6$ to both sides of the equation.

$8 x = 6$

Step 6

Divide each term in $8 x = 6$ by $8$ and simplify.

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Step 6.1

Divide each term in $8 x = 6$ by $8$ .

$\frac{8 x}{8} = \frac{6}{8}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $8$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{6}{8}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{8}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $6$ and $8$ .

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Step 6.3.1.1

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{8}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 3}{2 \cdot 4}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 4}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$