Algebra Examples

$- \frac{1}{2} (- 6 x - \frac{5}{2}) + 1 = 9 x$

Step 1

Simplify $- \frac{1}{2} \cdot (- 6 x - \frac{5}{2}) + 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- \frac{1}{2} (- 6 x) - \frac{1}{2} (- \frac{5}{2}) + 1 = 9 x$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

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

$\frac{- 1}{2} (- 6 x) - \frac{1}{2} (- \frac{5}{2}) + 1 = 9 x$

Step 1.1.2.2

Factor $2$ out of $- 6 x$ .

$\frac{- 1}{2} (2 (- 3 x)) - \frac{1}{2} (- \frac{5}{2}) + 1 = 9 x$

Step 1.1.2.3

Cancel the common factor.

$\frac{- 1}{2} (2 (- 3 x)) - \frac{1}{2} (- \frac{5}{2}) + 1 = 9 x$

Step 1.1.2.4

Rewrite the expression.

$- 1 (- 3 x) - \frac{1}{2} (- \frac{5}{2}) + 1 = 9 x$

Step 1.1.3

Multiply $- 3$ by $- 1$ .

$3 x - \frac{1}{2} (- \frac{5}{2}) + 1 = 9 x$

Step 1.1.4

Multiply $- \frac{1}{2} (- \frac{5}{2})$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

$3 x + 1 (\frac{1}{2}) \frac{5}{2} + 1 = 9 x$

Step 1.1.4.2

Multiply $\frac{1}{2}$ by $1$ .

$3 x + \frac{1}{2} \cdot \frac{5}{2} + 1 = 9 x$

Step 1.1.4.3

Multiply $\frac{1}{2}$ by $\frac{5}{2}$ .

$3 x + \frac{5}{2 \cdot 2} + 1 = 9 x$

Step 1.1.4.4

Multiply $2$ by $2$ .

$3 x + \frac{5}{4} + 1 = 9 x$

Step 1.2

Simplify the expression.

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$3 x + \frac{5}{4} + \frac{4}{4} = 9 x$

Step 1.2.2

Combine the numerators over the common denominator.

$3 x + \frac{5 + 4}{4} = 9 x$

Step 1.2.3

Add $5$ and $4$ .

$3 x + \frac{9}{4} = 9 x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $9 x$ from both sides of the equation.

$3 x + \frac{9}{4} - 9 x = 0$

Step 2.2

Subtract $9 x$ from $3 x$ .

$- 6 x + \frac{9}{4} = 0$

Step 3

Subtract $\frac{9}{4}$ from both sides of the equation.

$- 6 x = - \frac{9}{4}$

Step 4

Divide each term in $- 6 x = - \frac{9}{4}$ by $- 6$ and simplify.

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Step 4.1

Divide each term in $- 6 x = - \frac{9}{4}$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- \frac{9}{4}}{- 6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- \frac{9}{4}}{- 6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{9}{4}}{- 6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{9}{4} \cdot \frac{1}{- 6}$

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$x = \frac{- 9}{4} \cdot \frac{1}{- 6}$

Step 4.3.2.2

Factor $3$ out of $- 9$ .

$x = \frac{3 (- 3)}{4} \cdot \frac{1}{- 6}$

Step 4.3.2.3

Factor $3$ out of $- 6$ .

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

Step 4.3.2.4

Cancel the common factor.

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

Step 4.3.2.5

Rewrite the expression.

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

Step 4.3.3

Multiply $\frac{- 3}{4}$ by $\frac{1}{- 2}$ .

$x = \frac{- 3}{4 \cdot - 2}$

Step 4.3.4

Multiply $4$ by $- 2$ .

$x = \frac{- 3}{- 8}$

Step 4.3.5

Dividing two negative values results in a positive value.

$x = \frac{3}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{8}$

Decimal Form:

$x = 0.375$