Algebra Examples

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

Step 1

Simplify $- \frac{1}{4} \cdot (- 4 x - 6) - 6$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Cancel the common factor of $4$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 1.1.2.2

Factor $4$ out of $- 4 x$ .

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

Step 1.1.2.3

Cancel the common factor.

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

Step 1.1.2.4

Rewrite the expression.

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

Step 1.1.3

Multiply $- 1$ by $- 1$ .

$1 x - \frac{1}{4} \cdot - 6 - 6 = - \frac{1}{2} x$

Step 1.1.4

Multiply $x$ by $1$ .

$x - \frac{1}{4} \cdot - 6 - 6 = - \frac{1}{2} x$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$x + \frac{- 1}{4} \cdot - 6 - 6 = - \frac{1}{2} x$

Step 1.1.5.2

Factor $2$ out of $4$ .

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

Step 1.1.5.3

Factor $2$ out of $- 6$ .

$x + \frac{- 1}{2 \cdot 2} \cdot (2 \cdot - 3) - 6 = - \frac{1}{2} x$

Step 1.1.5.4

Cancel the common factor.

$x + \frac{- 1}{2 \cdot 2} \cdot (2 \cdot - 3) - 6 = - \frac{1}{2} x$

Step 1.1.5.5

Rewrite the expression.

$x + \frac{- 1}{2} \cdot - 3 - 6 = - \frac{1}{2} x$

Step 1.1.6

Combine $\frac{- 1}{2}$ and $- 3$ .

$x + \frac{- - 3}{2} - 6 = - \frac{1}{2} x$

Step 1.1.7

Multiply $- 1$ by $- 3$ .

$x + \frac{3}{2} - 6 = - \frac{1}{2} x$

Step 1.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x + \frac{3}{2} - 6 \cdot \frac{2}{2} = - \frac{1}{2} x$

Step 1.3

Combine $- 6$ and $\frac{2}{2}$ .

$x + \frac{3}{2} + \frac{- 6 \cdot 2}{2} = - \frac{1}{2} x$

Step 1.4

Combine the numerators over the common denominator.

$x + \frac{3 - 6 \cdot 2}{2} = - \frac{1}{2} x$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 6$ by $2$ .

$x + \frac{3 - 12}{2} = - \frac{1}{2} x$

Step 1.5.2

Subtract $12$ from $3$ .

$x + \frac{- 9}{2} = - \frac{1}{2} x$

Step 1.6

Move the negative in front of the fraction.

$x - \frac{9}{2} = - \frac{1}{2} x$

Step 2

Combine $x$ and $\frac{1}{2}$ .

$x - \frac{9}{2} = - \frac{x}{2}$

Step 3

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

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Step 3.1

Add $\frac{x}{2}$ to both sides of the equation.

$x - \frac{9}{2} + \frac{x}{2} = 0$

Step 3.2

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

$x \cdot \frac{2}{2} + \frac{x}{2} - \frac{9}{2} = 0$

Step 3.3

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

$\frac{x \cdot 2}{2} + \frac{x}{2} - \frac{9}{2} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{2} - \frac{9}{2} = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x - 9}{2} = 0$

Step 3.6

Move $2$ to the left of $x$ .

$\frac{2 x + x - 9}{2} = 0$

Step 3.7

Add $2 x$ and $x$ .

$\frac{3 x - 9}{2} = 0$

Step 3.8

Factor $3$ out of $3 x - 9$ .

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Step 3.8.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 9}{2} = 0$

Step 3.8.2

Factor $3$ out of $- 9$ .

$\frac{3 x + 3 \cdot - 3}{2} = 0$

Step 3.8.3

Factor $3$ out of $3 x + 3 \cdot - 3$ .

$\frac{3 (x - 3)}{2} = 0$

Step 4

Set the numerator equal to zero.

$3 (x - 3) = 0$

Step 5

Solve the equation for $x$ .

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Step 5.1

Divide each term in $3 (x - 3) = 0$ by $3$ and simplify.

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Step 5.1.1

Divide each term in $3 (x - 3) = 0$ by $3$ .

$\frac{3 (x - 3)}{3} = \frac{0}{3}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $3$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{3 (x - 3)}{3} = \frac{0}{3}$

Step 5.1.2.1.2

Divide $x - 3$ by $1$ .

$x - 3 = \frac{0}{3}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Divide $0$ by $3$ .

$x - 3 = 0$

Step 5.2

Add $3$ to both sides of the equation.

$x = 3$