Algebra Examples

3 | x - 4 | = 10

$3 | x - 4 | = 10$

Step 1

Divide each term in

3 | x - 4 | = 10

$3 | x - 4 | = 10$ by

3

$3$ and simplify.

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Step 1.1

Divide each term in

3 | x - 4 | = 10

$3 | x - 4 | = 10$ by

3

$3$ .

\frac{3 | x - 4 |}{3} = \frac{10}{3}

$\frac{3 | x - 4 |}{3} = \frac{10}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

3

$3$ .

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Step 1.2.1.1

Cancel the common factor.

\frac{3 | x - 4 |}{3} = \frac{10}{3}

$\frac{3 | x - 4 |}{3} = \frac{10}{3}$

Step 1.2.1.2

Divide

| x - 4 |

$| x - 4 |$ by

1

$1$ .

| x - 4 | = \frac{10}{3}

$| x - 4 | = \frac{10}{3}$

| x - 4 | = \frac{10}{3}

$| x - 4 | = \frac{10}{3}$

| x - 4 | = \frac{10}{3}

$| x - 4 | = \frac{10}{3}$

| x - 4 | = \frac{10}{3}

$| x - 4 | = \frac{10}{3}$

Step 2

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

x - 4 = \pm \frac{10}{3}

$x - 4 = \pm \frac{10}{3}$

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

$\pm$ to find the first solution.

x - 4 = \frac{10}{3}

$x - 4 = \frac{10}{3}$

Step 3.2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 3.2.1

Add

4

$4$ to both sides of the equation.

x = \frac{10}{3} + 4

$x = \frac{10}{3} + 4$

Step 3.2.2

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

x = \frac{10}{3} + 4 \cdot \frac{3}{3}

$x = \frac{10}{3} + 4 \cdot \frac{3}{3}$

Step 3.2.3

Combine

4

$4$ and

\frac{3}{3}

$\frac{3}{3}$ .

x = \frac{10}{3} + \frac{4 \cdot 3}{3}

$x = \frac{10}{3} + \frac{4 \cdot 3}{3}$

Step 3.2.4

Combine the numerators over the common denominator.

x = \frac{10 + 4 \cdot 3}{3}

$x = \frac{10 + 4 \cdot 3}{3}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply

4

$4$ by

3

$3$ .

x = \frac{10 + 12}{3}

$x = \frac{10 + 12}{3}$

Step 3.2.5.2

Add

10

$10$ and

12

$12$ .

x = \frac{22}{3}

$x = \frac{22}{3}$

x = \frac{22}{3}

$x = \frac{22}{3}$

x = \frac{22}{3}

$x = \frac{22}{3}$

Step 3.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x - 4 = - \frac{10}{3}

$x - 4 = - \frac{10}{3}$

Step 3.4

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 3.4.1

Add

4

$4$ to both sides of the equation.

x = - \frac{10}{3} + 4

$x = - \frac{10}{3} + 4$

Step 3.4.2

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

x = - \frac{10}{3} + 4 \cdot \frac{3}{3}

$x = - \frac{10}{3} + 4 \cdot \frac{3}{3}$

Step 3.4.3

Combine

4

$4$ and

\frac{3}{3}

$\frac{3}{3}$ .

x = - \frac{10}{3} + \frac{4 \cdot 3}{3}

$x = - \frac{10}{3} + \frac{4 \cdot 3}{3}$

Step 3.4.4

Combine the numerators over the common denominator.

x = \frac{- 10 + 4 \cdot 3}{3}

$x = \frac{- 10 + 4 \cdot 3}{3}$

Step 3.4.5

Simplify the numerator.

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Step 3.4.5.1

Multiply

4

$4$ by

3

$3$ .

x = \frac{- 10 + 12}{3}

$x = \frac{- 10 + 12}{3}$

Step 3.4.5.2

Add

- 10

$- 10$ and

12

$12$ .

x = \frac{2}{3}

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

x = \frac{2}{3}

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

x = \frac{2}{3}

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

Step 3.5

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

x = \frac{22}{3}, \frac{2}{3}

$x = \frac{22}{3}, \frac{2}{3}$

x = \frac{22}{3}, \frac{2}{3}

$x = \frac{22}{3}, \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \frac{22}{3}, \frac{2}{3}

$x = \frac{22}{3}, \frac{2}{3}$

Decimal Form:

x = 7.\overline{3}, 0.\overline{6}

$x = 7.\overline{3}, 0.\overline{6}$

Mixed Number Form:

x = 7 \frac{1}{3}, \frac{2}{3}

$x = 7 \frac{1}{3}, \frac{2}{3}$