Question

1. you try it! - solve and graph the compound inequality. -2(x + 1) < 4 and 4x + 1 ≤ -3

Explanation:

Step1: Solve the first - inequality

Solve $-2(x + 1)<4$.
First, distribute the $-2$: $-2x-2 < 4$.
Then add $2$ to both sides: $-2x<4 + 2$, so $-2x<6$.
Divide both sides by $-2$. When dividing by a negative number, the inequality sign flips. So $x>-3$.

Step2: Solve the second - inequality

Solve $4x + 1\leq - 3$.
Subtract $1$ from both sides: $4x\leq-3 - 1$, so $4x\leq-4$.
Divide both sides by $4$: $x\leq-1$.

The solution of the compound inequality is the intersection of the solutions of the two inequalities. So the solution is $-3 < x\leq-1$.

To graph it:

• Draw a number line.
• Mark a open - circle at $x = - 3$ (because $x>-3$, the value $-3$ is not included).
• Mark a closed - circle at $x=-1$ (because $x\leq-1$, the value $-1$ is included).
• Shade the region between the two points.

Answer:

The solution of the compound inequality is $-3 < x\leq-1$. The graph has an open - circle at $x = - 3$, a closed - circle at $x=-1$, and the region between them is shaded.