Algebra Examples

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

Step 1

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

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Step 1.1

Add $1$ to both sides of the equation.

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

Step 1.2

Add $62$ and $1$ .

$7 | 12 x + 3 | = 63$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

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.

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Step 4.1

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

$12 x + 3 = 9$

Step 4.2

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

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$12 x = 9 - 3$

Step 4.2.2

Subtract $3$ from $9$ .

$12 x = 6$

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $12$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $x$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

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

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Step 4.3.3.1.1

Factor $6$ out of $6$ .

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

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $6$ out of $12$ .

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

Step 4.3.3.1.2.2

Cancel the common factor.

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

Step 4.3.3.1.2.3

Rewrite the expression.

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

Step 4.4

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

$12 x + 3 = - 9$

Step 4.5

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

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Step 4.5.1

Subtract $3$ from both sides of the equation.

$12 x = - 9 - 3$

Step 4.5.2

Subtract $3$ from $- 9$ .

$12 x = - 12$

Step 4.6

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

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Step 4.6.1

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

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

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $12$ .

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Step 4.6.2.1.1

Cancel the common factor.

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

Step 4.6.2.1.2

Divide $x$ by $1$ .

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

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 12$ by $12$ .

$x = - 1$

Step 4.7

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:

$x = 0.5, - 1$