Question

solve the compound inequality. 4x + 5 < 9 and 3x + 2 ≥ -10 graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 5 from both sides of $4x + 5<9$:
$4x+5 - 5<9 - 5$, which simplifies to $4x<4$. Then divide both sides by 4: $x < 1$.

Step2: Solve the second inequality

Subtract 2 from both sides of $3x + 2\geq - 10$:
$3x+2-2\geq - 10 - 2$, which simplifies to $3x\geq - 12$. Then divide both sides by 3: $x\geq - 4$.

Answer:

The solution of the compound - inequality is $-4\leq x<1$. On the number line, we use a closed circle at $x = - 4$ (because $x$ can equal - 4) and an open circle at $x = 1$ (because $x$ cannot equal 1), and shade the region in between.