Question

Solve the inequality. Graph the solution set, and write it using interval notation. |5x+4|less than or equal to 10

Answer 1

we have the inequality

$\lvert5x+4\rvert\leq10$

step 1

Find out the first solution (positive case)

$\begin{gathered} +(5x+4)\leq10 \\ 5x\leq10-4 \\ 5x\leq6 \\ x\leq\frac{6}{5} \\ x\leq1.20 \end{gathered}$

The first solution is all real numbers less than or equal to 1.20

Interval (-infinite,1.20]

step 2

Find out the second solution (negative case)

$-(5x+4)\leq10$

Multiply by -1 both sides

$\begin{gathered} (5x+4)\ge-10 \\ 5x\ge-10-4 \\ 5x\ge-14 \\ x\ge-\frac{14}{5} \\ x\ge-2.8 \end{gathered}$

The second solution is all real numbers greater than or equal to -2.8

the interval [-2.8, infinite)

step 3

Find out the solution to the given inequality

The solution is

[-2.8, infinite) ∩ (-infinite,1.20]=[-2.8,1.20]

the solution is the interval [-2.8,1.20]

see the attached figure to better understand the problem