Algebra Examples

$\frac{3}{4} (- 5 x - 8) = - 6 (x + 4) + \frac{1}{4} x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 6 (x + 4) + \frac{1}{4} x = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 6 x - 6 \cdot 4 + \frac{1}{4} x = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.1.2

Multiply $- 6$ by $4$ .

$- 6 x - 24 + \frac{1}{4} x = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.1.3

Combine $\frac{1}{4}$ and $x$ .

$- 6 x - 24 + \frac{x}{4} = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.2

To write $- 6 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 6 x \cdot \frac{4}{4} + \frac{x}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $- 6 x$ and $\frac{4}{4}$ .

$\frac{- 6 x \cdot 4}{4} + \frac{x}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{- 6 x \cdot 4 + x}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $x$ out of $- 6 x \cdot 4 + x$ .

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Step 2.4.1.1.1

Factor $x$ out of $- 6 x \cdot 4$ .

$\frac{x (- 6 \cdot 4) + x}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.1.1.2

Raise $x$ to the power of $1$ .

$\frac{x (- 6 \cdot 4) + x^{1}}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.1.1.3

Factor $x$ out of $x^{1}$ .

$\frac{x (- 6 \cdot 4) + x \cdot 1}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.1.1.4

Factor $x$ out of $x (- 6 \cdot 4) + x \cdot 1$ .

$\frac{x (- 6 \cdot 4 + 1)}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.1.2

Multiply $- 6$ by $4$ .

$\frac{x (- 24 + 1)}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.1.3

Add $- 24$ and $1$ .

$\frac{x \cdot - 23}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.2

Move $- 23$ to the left of $x$ .

$\frac{- 23 \cdot x}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 2.4.3

Move the negative in front of the fraction.

$- \frac{23 x}{4} - 24 = \frac{3}{4} \cdot (- 5 x - 8)$

Step 3

Simplify $\frac{3}{4} \cdot (- 5 x - 8)$ .

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Step 3.1

Apply the distributive property.

$- \frac{23 x}{4} - 24 = \frac{3}{4} (- 5 x) + \frac{3}{4} \cdot - 8$

Step 3.2

Multiply $\frac{3}{4} (- 5 x)$ .

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Step 3.2.1

Combine $- 5$ and $\frac{3}{4}$ .

$- \frac{23 x}{4} - 24 = \frac{- 5 \cdot 3}{4} x + \frac{3}{4} \cdot - 8$

Step 3.2.2

Multiply $- 5$ by $3$ .

$- \frac{23 x}{4} - 24 = \frac{- 15}{4} x + \frac{3}{4} \cdot - 8$

Step 3.2.3

Combine $\frac{- 15}{4}$ and $x$ .

$- \frac{23 x}{4} - 24 = \frac{- 15 x}{4} + \frac{3}{4} \cdot - 8$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Factor $4$ out of $- 8$ .

$- \frac{23 x}{4} - 24 = \frac{- 15 x}{4} + \frac{3}{4} \cdot (4 (- 2))$

Step 3.3.2

Cancel the common factor.

$- \frac{23 x}{4} - 24 = \frac{- 15 x}{4} + \frac{3}{4} \cdot (4 \cdot - 2)$

Step 3.3.3

Rewrite the expression.

$- \frac{23 x}{4} - 24 = \frac{- 15 x}{4} + 3 \cdot - 2$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $3$ by $- 2$ .

$- \frac{23 x}{4} - 24 = \frac{- 15 x}{4} - 6$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{23 x}{4} - 24 = - \frac{15 x}{4} - 6$

Step 4

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

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Step 4.1

Add $\frac{15 x}{4}$ to both sides of the equation.

$- \frac{23 x}{4} - 24 + \frac{15 x}{4} = - 6$

Step 4.2

Combine the numerators over the common denominator.

$- 24 + \frac{- 23 x + 15 x}{4} = - 6$

Step 4.3

Add $- 23 x$ and $15 x$ .

$- 24 + \frac{- 8 x}{4} = - 6$

Step 4.4

Cancel the common factor of $- 8$ and $4$ .

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Step 4.4.1

Factor $4$ out of $- 8 x$ .

$- 24 + \frac{4 (- 2 x)}{4} = - 6$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $4$ out of $4$ .

$- 24 + \frac{4 (- 2 x)}{4 (1)} = - 6$

Step 4.4.2.2

Cancel the common factor.

$- 24 + \frac{4 (- 2 x)}{4 \cdot 1} = - 6$

Step 4.4.2.3

Rewrite the expression.

$- 24 + \frac{- 2 x}{1} = - 6$

Step 4.4.2.4

Divide $- 2 x$ by $1$ .

$- 24 - 2 x = - 6$

Step 5

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

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Step 5.1

Add $24$ to both sides of the equation.

$- 2 x = - 6 + 24$

Step 5.2

Add $- 6$ and $24$ .

$- 2 x = 18$

Step 6

Divide each term in $- 2 x = 18$ by $- 2$ and simplify.

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Step 6.1

Divide each term in $- 2 x = 18$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{18}{- 2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{18}{- 2}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{- 2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $18$ by $- 2$ .

$x = - 9$