Algebra Examples

$4 (5 x + 7) \leq 13$

Step 1

Solve $x \leq - \frac{3}{4}$ .

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Step 1.1

Divide each term in $4 (5 x + 7) \leq 13$ by $4$ and simplify.

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Step 1.1.1

Divide each term in $4 (5 x + 7) \leq 13$ by $4$ .

$\frac{4 (5 x + 7)}{4} \leq \frac{13}{4}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $4$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{4 (5 x + 7)}{4} \leq \frac{13}{4}$

Step 1.1.2.1.2

Divide $5 x + 7$ by $1$ .

$5 x + 7 \leq \frac{13}{4}$

Step 1.2

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

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Step 1.2.1

Subtract $7$ from both sides of the inequality.

$5 x \leq \frac{13}{4} - 7$

Step 1.2.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$5 x \leq \frac{13}{4} - 7 \cdot \frac{4}{4}$

Step 1.2.3

Combine $- 7$ and $\frac{4}{4}$ .

$5 x \leq \frac{13}{4} + \frac{- 7 \cdot 4}{4}$

Step 1.2.4

Combine the numerators over the common denominator.

$5 x \leq \frac{13 - 7 \cdot 4}{4}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $- 7$ by $4$ .

$5 x \leq \frac{13 - 28}{4}$

Step 1.2.5.2

Subtract $28$ from $13$ .

$5 x \leq \frac{- 15}{4}$

Step 1.2.6

Move the negative in front of the fraction.

$5 x \leq - \frac{15}{4}$

Step 1.3

Divide each term in $5 x \leq - \frac{15}{4}$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 x \leq - \frac{15}{4}$ by $5$ .

$\frac{5 x}{5} \leq \frac{- \frac{15}{4}}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{- \frac{15}{4}}{5}$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- \frac{15}{4}}{5}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x \leq - \frac{15}{4} \cdot \frac{1}{5}$

Step 1.3.3.2

Cancel the common factor of $5$ .

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Step 1.3.3.2.1

Move the leading negative in $- \frac{15}{4}$ into the numerator.

$x \leq \frac{- 15}{4} \cdot \frac{1}{5}$

Step 1.3.3.2.2

Factor $5$ out of $- 15$ .

$x \leq \frac{5 (- 3)}{4} \cdot \frac{1}{5}$

Step 1.3.3.2.3

Cancel the common factor.

$x \leq \frac{5 \cdot - 3}{4} \cdot \frac{1}{5}$

Step 1.3.3.2.4

Rewrite the expression.

$x \leq \frac{- 3}{4}$

Step 1.3.3.3

Move the negative in front of the fraction.

$x \leq - \frac{3}{4}$

Step 2

Use the inequality $x \leq - \frac{3}{4}$ to build the set notation.

${x | x \leq - \frac{3}{4}}$

Step 3