Question

Solve the compound inequality.3 – 2x ≥ 5 or 3(x – 2) + 1 > 7A.x ≤ – 4 or x < 1B.x ≥ – 4 or x < 1C.x ≤ –1 or x > 4D.x ≥ –1 or x > 4

Answer 1

C. x ≤ -1 or x > 4

Step-by-step explanation:

We need to solve both inequalities. For the first one, we get:

3 - 2x ≥ 5

Subtract 3 from both sides:

3 - 2x - 3 ≥ 5 - 3

-2x ≥ 2

Divide both sides by -2. Since -2 is negative the sign will change, so:

-2x/(-2) ≤ 2/(-2)

x ≤ -1

Now, we can solve the second inequality, so:

3(x - 2) + 1 > 7

Apply the distributive property:

3x - 3(2) + 1 > 7

3x - 6 + 1 > 7

3x - 5 > 7

Add 5 to both sides:

3x - 5 + 5 > 7 + 5

3x > 12

Finally, divide by 3:

3x/3 > 12/3

x > 4

Therefore, the solution of the compound inequality is:

C. x ≤ -1 or x > 4