Convert to Interval Notation 11<=5x-4<=31

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Trigonometry

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

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

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

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

Add $11$ and $4$ .

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

Add $31$ and $4$ .

$15 \leq 5 x \leq 35$

Divide each term in the inequality by $5$ .

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

Divide $15$ by $5$ .

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

Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $35$ by $5$ .

$3 \leq x \leq 7$

Convert the inequality to interval notation.

$[3, 7]$

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