Algebra Examples

$3 - 5 | 10 - 4 x | = - 57$

Step 1

Move all terms not containing $| 10 - 4 x |$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$- 5 | 10 - 4 x | = - 57 - 3$

Step 1.2

Subtract $3$ from $- 57$ .

$- 5 | 10 - 4 x | = - 60$

Step 2

Divide each term in $- 5 | 10 - 4 x | = - 60$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 | 10 - 4 x | = - 60$ by $- 5$ .

$\frac{- 5 | 10 - 4 x |}{- 5} = \frac{- 60}{- 5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 5 | 10 - 4 x |}{- 5} = \frac{- 60}{- 5}$

Step 2.2.1.2

Divide $| 10 - 4 x |$ by $1$ .

$| 10 - 4 x | = \frac{- 60}{- 5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 60$ by $- 5$ .

$| 10 - 4 x | = 12$

Step 3

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

$10 - 4 x = \pm 12$

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.

$10 - 4 x = 12$

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 $10$ from both sides of the equation.

$- 4 x = 12 - 10$

Step 4.2.2

Subtract $10$ from $12$ .

$- 4 x = 2$

Step 4.3

Divide each term in $- 4 x = 2$ by $- 4$ and simplify.

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Step 4.3.1

Divide each term in $- 4 x = 2$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{2}{- 4}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{- 4}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $2$ and $- 4$ .

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Step 4.3.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{- 4}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $2$ out of $- 4$ .

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

Step 4.3.3.1.2.2

Cancel the common factor.

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

Step 4.3.3.1.2.3

Rewrite the expression.

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

Step 4.3.3.2

Move the negative in front of the fraction.

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

Step 4.4

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

$10 - 4 x = - 12$

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 $10$ from both sides of the equation.

$- 4 x = - 12 - 10$

Step 4.5.2

Subtract $10$ from $- 12$ .

$- 4 x = - 22$

Step 4.6

Divide each term in $- 4 x = - 22$ by $- 4$ and simplify.

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Step 4.6.1

Divide each term in $- 4 x = - 22$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 22}{- 4}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $- 4$ .

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Step 4.6.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 22}{- 4}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 22}{- 4}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Cancel the common factor of $- 22$ and $- 4$ .

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Step 4.6.3.1.1

Factor $- 2$ out of $- 22$ .

$x = \frac{- 2 (11)}{- 4}$

Step 4.6.3.1.2

Cancel the common factors.

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Step 4.6.3.1.2.1

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

$x = \frac{- 2 \cdot 11}{- 2 \cdot 2}$

Step 4.6.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 11}{- 2 \cdot 2}$

Step 4.6.3.1.2.3

Rewrite the expression.

$x = \frac{11}{2}$

Step 4.7

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

$x = - \frac{1}{2}, \frac{11}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, \frac{11}{2}$

Decimal Form:

$x = - 0.5, 5.5$

Mixed Number Form:

$x = - \frac{1}{2}, 5 \frac{1}{2}$