Question

what is the solution to the compound inequality
$5x + 7 \geq -8$ and $3x + 7 < 19$
\bigcirc $-3 \leq x < 4$
\bigcirc $-3 < x < 4$
\bigcirc $x \leq -3$ and $x \geq 4$
\bigcirc $x > -3$ and $x > 4$

Explanation:

Step1: Solve \(5x + 7\geq - 8\)

Subtract 7 from both sides: \(5x\geq - 8 - 7\)
Simplify: \(5x\geq - 15\)
Divide by 5: \(x\geq - 3\)

Step2: Solve \(3x + 7\lt19\)

Subtract 7 from both sides: \(3x\lt19 - 7\)
Simplify: \(3x\lt12\)
Divide by 3: \(x\lt4\)

Step3: Combine the solutions

From step 1, \(x\geq - 3\); from step 2, \(x\lt4\). So the solution is \(-3\leq x\lt4\)

Answer:

\(-3\leq x\lt4\) (corresponding to the first option: \(\boldsymbol{-3 \leq x < 4}\))