Question

Find the number of integers in the solution set of $|4x+3|<8$.

• A. None
• B. Two
• C. Three
• D. Four
• E. Infinitely many

Answer 1

The correct option is D Four

Rule is when $|y|<a$

$\Rightarrow -a<y<a$

Now when $|4x+3|<8$, then

$-8<4x+3<8$

Subtracting $3$ from the inequality, we get

$-8-3<4x<8-3$

$-11<4x<5$

$\Rightarrow -2.75<x<1.25$

So, $x$ has $4$ possible integer values: $-2,-1,0,1$.