Solve the Absolute Value Inequality for x 7|12x+3|-1=62

$7 | 12 x + 3 | - 1 = 62$

Step 1

Move all terms not containing $| 12 x + 3 |$ to the right side of the equation.

Add $1$ to both sides of the equation.

$7 | 12 x + 3 | = 62 + 1$

Add $62$ and $1$ .

$7 | 12 x + 3 | = 63$

Step 2

Divide each term in $7 | 12 x + 3 | = 63$ by $7$ and simplify.

Divide each term in $7 | 12 x + 3 | = 63$ by $7$ .

$\frac{7 | 12 x + 3 |}{7} = \frac{63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 | 12 x + 3 |}{7} = \frac{63}{7}$

Divide $| 12 x + 3 |$ by $1$ .

$| 12 x + 3 | = \frac{63}{7}$

Simplify the right side.

Divide $63$ by $7$ .

$| 12 x + 3 | = 9$

Step 3

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

$12 x + 3 = \pm 9$

Step 4

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

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

$12 x + 3 = 9$

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

Subtract $3$ from both sides of the equation.

$12 x = 9 - 3$

Subtract $3$ from $9$ .

$12 x = 6$

Divide each term in $12 x = 6$ by $12$ and simplify.

Divide each term in $12 x = 6$ by $12$ .

$\frac{12 x}{12} = \frac{6}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{6}{12}$

Divide $x$ by $1$ .

$x = \frac{6}{12}$

Simplify the right side.

Cancel the common factor of $6$ and $12$ .

Factor $6$ out of $6$ .

$x = \frac{6 (1)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 1}{6 \cdot 2}$

Cancel the common factor.

$x = \frac{6 \cdot 1}{6 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

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

$12 x + 3 = - 9$

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

Subtract $3$ from both sides of the equation.

$12 x = - 9 - 3$

Subtract $3$ from $- 9$ .

$12 x = - 12$

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

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

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

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 12$ by $12$ .

$x = - 1$

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

$x = \frac{1}{2}, - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - 1$

Decimal Form:

$x = 0.5, - 1$

Solve the Absolute Value Inequality for x 7|12x+3|-1=62

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