Algebra Examples

$3 - 2 | 0.5 x + 1.5 | = 2$

Step 1

Move all terms not containing $| 0.5 x + 1.5 |$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$- 2 | 0.5 x + 1.5 | = 2 - 3$

Step 1.2

Subtract $3$ from $2$ .

$- 2 | 0.5 x + 1.5 | = - 1$

Step 2

Divide each term in $- 2 | 0.5 x + 1.5 | = - 1$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 | 0.5 x + 1.5 | = - 1$ by $- 2$ .

$\frac{- 2 | 0.5 x + 1.5 |}{- 2} = \frac{- 1}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 | 0.5 x + 1.5 |}{- 2} = \frac{- 1}{- 2}$

Step 2.2.1.2

Divide $| 0.5 x + 1.5 |$ by $1$ .

$| 0.5 x + 1.5 | = \frac{- 1}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

$| 0.5 x + 1.5 | = \frac{1}{2}$

Step 3

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

$0.5 x + 1.5 = \pm \frac{1}{2}$

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.

$0.5 x + 1.5 = \frac{1}{2}$

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 $1.5$ from both sides of the equation.

$0.5 x = \frac{1}{2} - 1.5$

Step 4.2.2

To write $- 1.5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$0.5 x = \frac{1}{2} - 1.5 \cdot \frac{2}{2}$

Step 4.2.3

Combine $- 1.5$ and $\frac{2}{2}$ .

$0.5 x = \frac{1}{2} + \frac{- 1.5 \cdot 2}{2}$

Step 4.2.4

Combine the numerators over the common denominator.

$0.5 x = \frac{1 - 1.5 \cdot 2}{2}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 1.5$ by $2$ .

$0.5 x = \frac{1 - 3}{2}$

Step 4.2.5.2

Subtract $3$ from $1$ .

$0.5 x = \frac{- 2}{2}$

Step 4.2.6

Divide $- 2$ by $2$ .

$0.5 x = - 1$

Step 4.3

Divide each term in $0.5 x = - 1$ by $0.5$ and simplify.

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Step 4.3.1

Divide each term in $0.5 x = - 1$ by $0.5$ .

$\frac{0.5 x}{0.5} = \frac{- 1}{0.5}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $0.5$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{0.5 x}{0.5} = \frac{- 1}{0.5}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{0.5}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 1$ by $0.5$ .

$x = - 2$

Step 4.4

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

$0.5 x + 1.5 = - \frac{1}{2}$

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 $1.5$ from both sides of the equation.

$0.5 x = - \frac{1}{2} - 1.5$

Step 4.5.2

To write $- 1.5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$0.5 x = - \frac{1}{2} - 1.5 \cdot \frac{2}{2}$

Step 4.5.3

Combine $- 1.5$ and $\frac{2}{2}$ .

$0.5 x = - \frac{1}{2} + \frac{- 1.5 \cdot 2}{2}$

Step 4.5.4

Combine the numerators over the common denominator.

$0.5 x = \frac{- 1 - 1.5 \cdot 2}{2}$

Step 4.5.5

Simplify the numerator.

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Step 4.5.5.1

Multiply $- 1.5$ by $2$ .

$0.5 x = \frac{- 1 - 3}{2}$

Step 4.5.5.2

Subtract $3$ from $- 1$ .

$0.5 x = \frac{- 4}{2}$

Step 4.5.6

Divide $- 4$ by $2$ .

$0.5 x = - 2$

Step 4.6

Divide each term in $0.5 x = - 2$ by $0.5$ and simplify.

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Step 4.6.1

Divide each term in $0.5 x = - 2$ by $0.5$ .

$\frac{0.5 x}{0.5} = \frac{- 2}{0.5}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $0.5$ .

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Step 4.6.2.1.1

Cancel the common factor.

$\frac{0.5 x}{0.5} = \frac{- 2}{0.5}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{0.5}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 2$ by $0.5$ .

$x = - 4$

Step 4.7

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

$x = - 2, - 4$