Trigonometry Examples

$11 \leq 5 x - 4 \leq 31$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

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Step 1.1

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$11 + 4 \leq 5 x \leq 31 + 4$

Step 1.2

Add $11$ and $4$ .

$15 \leq 5 x \leq 31 + 4$

Step 1.3

Add $31$ and $4$ .

$15 \leq 5 x \leq 35$

Step 2

Divide each term in the inequality by $5$ .

$\frac{15}{5} \leq \frac{5 x}{5} \leq \frac{35}{5}$

Step 3

Divide $15$ by $5$ .

$3 \leq \frac{5 x}{5} \leq \frac{35}{5}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

$3 \leq \frac{5 x}{5} \leq \frac{35}{5}$

Step 4.2

Divide $x$ by $1$ .

$3 \leq x \leq \frac{35}{5}$

Step 5

Divide $35$ by $5$ .

$3 \leq x \leq 7$

Step 6

Convert the inequality to interval notation.

$[3, 7]$

Step 7