Precalculus Examples

$\frac{3}{2} \cdot (x + 5) - \frac{1}{4} \cdot (x + 24) = 0$

Step 1

Simplify $\frac{3}{2} \cdot (x + 5) - \frac{1}{4} \cdot (x + 24)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{3}{2} x + \frac{3}{2} \cdot 5 - \frac{1}{4} \cdot (x + 24) = 0$

Step 1.1.2

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

$\frac{3 x}{2} + \frac{3}{2} \cdot 5 - \frac{1}{4} \cdot (x + 24) = 0$

Step 1.1.3

Multiply $\frac{3}{2} \cdot 5$ .

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Step 1.1.3.1

Combine $\frac{3}{2}$ and $5$ .

$\frac{3 x}{2} + \frac{3 \cdot 5}{2} - \frac{1}{4} \cdot (x + 24) = 0$

Step 1.1.3.2

Multiply $3$ by $5$ .

$\frac{3 x}{2} + \frac{15}{2} - \frac{1}{4} \cdot (x + 24) = 0$

Step 1.1.4

Apply the distributive property.

$\frac{3 x}{2} + \frac{15}{2} - \frac{1}{4} x - \frac{1}{4} \cdot 24 = 0$

Step 1.1.5

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

$\frac{3 x}{2} + \frac{15}{2} - \frac{x}{4} - \frac{1}{4} \cdot 24 = 0$

Step 1.1.6

Cancel the common factor of $4$ .

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Step 1.1.6.1

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

$\frac{3 x}{2} + \frac{15}{2} - \frac{x}{4} + \frac{- 1}{4} \cdot 24 = 0$

Step 1.1.6.2

Factor $4$ out of $24$ .

$\frac{3 x}{2} + \frac{15}{2} - \frac{x}{4} + \frac{- 1}{4} \cdot (4 (6)) = 0$

Step 1.1.6.3

Cancel the common factor.

$\frac{3 x}{2} + \frac{15}{2} - \frac{x}{4} + \frac{- 1}{4} \cdot (4 \cdot 6) = 0$

Step 1.1.6.4

Rewrite the expression.

$\frac{3 x}{2} + \frac{15}{2} - \frac{x}{4} - 1 \cdot 6 = 0$

Step 1.1.7

Multiply $- 1$ by $6$ .

$\frac{3 x}{2} + \frac{15}{2} - \frac{x}{4} - 6 = 0$

Step 1.2

To write $\frac{3 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} \cdot \frac{2}{2} - \frac{x}{4} + \frac{15}{2} - 6 = 0$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 x}{2}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2}{2 \cdot 2} - \frac{x}{4} + \frac{15}{2} - 6 = 0$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{3 x \cdot 2}{4} - \frac{x}{4} + \frac{15}{2} - 6 = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - x}{4} + \frac{15}{2} - 6 = 0$

Step 1.5

Find the common denominator.

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Step 1.5.1

Multiply $\frac{15}{2}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2 - x}{4} + \frac{15}{2} \cdot \frac{2}{2} - 6 = 0$

Step 1.5.2

Multiply $\frac{15}{2}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2 - x}{4} + \frac{15 \cdot 2}{2 \cdot 2} - 6 = 0$

Step 1.5.3

Write $- 6$ as a fraction with denominator $1$ .

$\frac{3 x \cdot 2 - x}{4} + \frac{15 \cdot 2}{2 \cdot 2} + \frac{- 6}{1} = 0$

Step 1.5.4

Multiply $\frac{- 6}{1}$ by $\frac{4}{4}$ .

$\frac{3 x \cdot 2 - x}{4} + \frac{15 \cdot 2}{2 \cdot 2} + \frac{- 6}{1} \cdot \frac{4}{4} = 0$

Step 1.5.5

Multiply $\frac{- 6}{1}$ by $\frac{4}{4}$ .

$\frac{3 x \cdot 2 - x}{4} + \frac{15 \cdot 2}{2 \cdot 2} + \frac{- 6 \cdot 4}{4} = 0$

Step 1.5.6

Multiply $2$ by $2$ .

$\frac{3 x \cdot 2 - x}{4} + \frac{15 \cdot 2}{4} + \frac{- 6 \cdot 4}{4} = 0$

Step 1.6

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - x + 15 \cdot 2 - 6 \cdot 4}{4} = 0$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $2$ by $3$ .

$\frac{6 x - x + 15 \cdot 2 - 6 \cdot 4}{4} = 0$

Step 1.7.2

Multiply $15$ by $2$ .

$\frac{6 x - x + 30 - 6 \cdot 4}{4} = 0$

Step 1.7.3

Multiply $- 6$ by $4$ .

$\frac{6 x - x + 30 - 24}{4} = 0$

Step 1.8

Simplify by adding terms.

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Step 1.8.1

Subtract $x$ from $6 x$ .

$\frac{5 x + 30 - 24}{4} = 0$

Step 1.8.2

Subtract $24$ from $30$ .

$\frac{5 x + 6}{4} = 0$

Step 2

Set the numerator equal to zero.

$5 x + 6 = 0$

Step 3

Solve the equation for $x$ .

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Step 3.1

Subtract $6$ from both sides of the equation.

$5 x = - 6$

Step 3.2

Divide each term in $5 x = - 6$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 x = - 6$ by $5$ .

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.2$

Mixed Number Form:

$x = - 1 \frac{1}{5}$