Leon Bishop

2023-03-18

How to solve $|5x+3|\le 13$?

esberquemlrb4

Beginner2023-03-19Added 6 answers

The two inequalities below must be resolved because we are working with absolute value.

$5x+3\le 13$ and $-(5x+3)\le 13$

Solving the first one

Substract $3$ from both sides

$5x+3-3\le 13-3$

$5x\le 10$

Dividing by both sides by $5$

$x\le 2$

Now solving the second one

Move the negative sign to the left side of the equation.

$-5x-3\le 13$

Add $3$ to both sides

$-5x-3+3\le 13+3$

$-5x\le 16$

Divide both sides by $-5$

We must reverse the inequality sign because we are dividing through by a negative integer.

$x\ge -\frac{16}{5}$

$5x+3\le 13$ and $-(5x+3)\le 13$

Solving the first one

Substract $3$ from both sides

$5x+3-3\le 13-3$

$5x\le 10$

Dividing by both sides by $5$

$x\le 2$

Now solving the second one

Move the negative sign to the left side of the equation.

$-5x-3\le 13$

Add $3$ to both sides

$-5x-3+3\le 13+3$

$-5x\le 16$

Divide both sides by $-5$

We must reverse the inequality sign because we are dividing through by a negative integer.

$x\ge -\frac{16}{5}$

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