Question

Solve the compound inequality 4x - 7 > 5 or 5x + 4 ≤ -6.

a) x > 3
b) x ≤ -2
c) x ≤ -2 or x > 3
d) -2 ≤ x < 3

Answer 1

To solve the compound inequality, separate them into two inequalities: 4x - 7 > 5 and 5x + 4 ≤ -6. Solve each inequality to find x > 3 and x ≤ -2 respectively. The collective solution is x ≤ -2 or x > 3.

Step-by-step explanation:

To solve the compound inequality 4x - 7 > 5 or 5x + 4 ≤ -6, we'll tackle each inequality separately and then consider their union as the solution.

First, let's solve 4x - 7 > 5:

• Add 7 to both sides: 4x > 12.
• Divide both sides by 4: x > 3.

Next, let's solve 5x + 4 ≤ -6:

• Subtract 4 from both sides: 5x ≤ -10.
• Divide both sides by 5: x ≤ -2.

Combining these results, we have two parts to our solution: x > 3 or x ≤ -2. The correct response is x ≤ -2 or x > 3, which corresponds to the option (c).