Algebra Examples

$- 4 (\frac{3}{2} x - \frac{1}{2}) = - 15$

Step 1

Simplify $- 4 (\frac{3}{2} x - \frac{1}{2})$ .

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Step 1.1

Combine $\frac{3}{2}$ and $x$ .

$- 4 (\frac{3 x}{2} - \frac{1}{2}) = - 15$

Step 1.2

Apply the distributive property.

$- 4 \frac{3 x}{2} - 4 (- \frac{1}{2}) = - 15$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $- 4$ .

$2 (- 2) \frac{3 x}{2} - 4 (- \frac{1}{2}) = - 15$

Step 1.3.2

Cancel the common factor.

$2 \cdot - 2 \frac{3 x}{2} - 4 (- \frac{1}{2}) = - 15$

Step 1.3.3

Rewrite the expression.

$- 2 (3 x) - 4 (- \frac{1}{2}) = - 15$

Step 1.4

Multiply $3$ by $- 2$ .

$- 6 x - 4 (- \frac{1}{2}) = - 15$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 6 x - 4 (\frac{- 1}{2}) = - 15$

Step 1.5.2

Factor $2$ out of $- 4$ .

$- 6 x + 2 (- 2) \frac{- 1}{2} = - 15$

Step 1.5.3

Cancel the common factor.

$- 6 x + 2 \cdot - 2 \frac{- 1}{2} = - 15$

Step 1.5.4

Rewrite the expression.

$- 6 x - 2 \cdot - 1 = - 15$

Step 1.6

Multiply $- 2$ by $- 1$ .

$- 6 x + 2 = - 15$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$- 6 x = - 15 - 2$

Step 2.2

Subtract $2$ from $- 15$ .

$- 6 x = - 17$

Step 3

Divide each term in $- 6 x = - 17$ by $- 6$ and simplify.

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Step 3.1

Divide each term in $- 6 x = - 17$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 17}{- 6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 17}{- 6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 17}{- 6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$x = \frac{17}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{6}$

Decimal Form:

$x = 2.8\overline{3}$

Mixed Number Form:

$x = 2 \frac{5}{6}$