Question

solve the inequality and graph the solution. 3x - 2 ≥ 4 and 7 - 9x > -20 2 ≤ x < 3 -2 ≥ x > 3 2 ≥ x > 3 -2 ≤ x < 3

Explanation:

Step1: Solve the first inequality

Add 2 to both sides of $3x - 2\geq4$: $3x- 2+2\geq4 + 2$, which simplifies to $3x\geq6$. Then divide both sides by 3: $x\geq2$.

Step2: Solve the second inequality

Subtract 7 from both sides of $7 - 9x>-20$: $7-9x - 7>-20 - 7$, which gives $-9x>-27$. Divide both sides by - 9 and reverse the inequality sign: $x < 3$.

Step3: Combine the solutions

Since it is an "AND" compound - inequality, the solution is the intersection of the two solution sets, so $2\leq x<3$.

Answer:

The correct option is the one with the inequality $2\leq x<3$ and the graph having a closed - circle at 2 and an open - circle at 3 with the line segment in between them.