Basic Math Examples

$| - 4 d + 6 | = 12$

Step 1

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

$- 4 d + 6 = \pm 12$

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.

$- 4 d + 6 = 12$

Step 2.2

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

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Step 2.2.1

Subtract $6$ from both sides of the equation.

$- 4 d = 12 - 6$

Step 2.2.2

Subtract $6$ from $12$ .

$- 4 d = 6$

Step 2.3

Divide each term in $- 4 d = 6$ by $- 4$ and simplify.

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Step 2.3.1

Divide each term in $- 4 d = 6$ by $- 4$ .

$\frac{- 4 d}{- 4} = \frac{6}{- 4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 4 d}{- 4} = \frac{6}{- 4}$

Step 2.3.2.1.2

Divide $d$ by $1$ .

$d = \frac{6}{- 4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $6$ and $- 4$ .

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Step 2.3.3.1.1

Factor $2$ out of $6$ .

$d = \frac{2 (3)}{- 4}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $2$ out of $- 4$ .

$d = \frac{2 \cdot 3}{2 \cdot - 2}$

Step 2.3.3.1.2.2

Cancel the common factor.

$d = \frac{2 \cdot 3}{2 \cdot - 2}$

Step 2.3.3.1.2.3

Rewrite the expression.

$d = \frac{3}{- 2}$

Step 2.3.3.2

Move the negative in front of the fraction.

$d = - \frac{3}{2}$

Step 2.4

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

$- 4 d + 6 = - 12$

Step 2.5

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

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Step 2.5.1

Subtract $6$ from both sides of the equation.

$- 4 d = - 12 - 6$

Step 2.5.2

Subtract $6$ from $- 12$ .

$- 4 d = - 18$

Step 2.6

Divide each term in $- 4 d = - 18$ by $- 4$ and simplify.

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Step 2.6.1

Divide each term in $- 4 d = - 18$ by $- 4$ .

$\frac{- 4 d}{- 4} = \frac{- 18}{- 4}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $- 4$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{- 4 d}{- 4} = \frac{- 18}{- 4}$

Step 2.6.2.1.2

Divide $d$ by $1$ .

$d = \frac{- 18}{- 4}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Cancel the common factor of $- 18$ and $- 4$ .

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Step 2.6.3.1.1

Factor $- 2$ out of $- 18$ .

$d = \frac{- 2 (9)}{- 4}$

Step 2.6.3.1.2

Cancel the common factors.

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Step 2.6.3.1.2.1

Factor $- 2$ out of $- 4$ .

$d = \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Step 2.6.3.1.2.2

Cancel the common factor.

$d = \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Step 2.6.3.1.2.3

Rewrite the expression.

$d = \frac{9}{2}$

Step 2.7

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

$d = - \frac{3}{2}, \frac{9}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{3}{2}, \frac{9}{2}$

Decimal Form:

$d = - 1.5, 4.5$

Mixed Number Form:

$d = - 1 \frac{1}{2}, 4 \frac{1}{2}$