Question

Solve the inequality: 2(3a - 2) ≥ 4(a - 2).

a. a ≥ 0
b. a ≤ 0
c. a > 2
d. a < 2

Answer 1

To solve the inequality, distribute and simplify on both sides, isolate 'a', and solve for 'a'. The solution is 'a ≥ -2'.

Step-by-step explanation:

To solve the inequality, we need to simplify both sides and isolate 'a'.

Starting with the left side, distribute the '2' into the parentheses: 2*(3a - 2) = 6a - 4.

Now simplify the right side by distributing the '4' into the parentheses: 4*(a - 2) = 4a - 8.

Now the inequality becomes: 6a - 4 ≥ 4a - 8.

Next, subtract '4a' from both sides to get rid of the terms with 'a' on the right side: 6a - 4 - 4a ≥ -8.

This simplifies to: 2a - 4 ≥ -8.

Finally, add '4' to both sides to isolate 'a': 2a - 4 + 4 ≥ -8 + 4.

This results in: 2a ≥ -4.

Dividing both sides by '2', we get: a ≥ -2.

Therefore, the solution is 'a ≥ -2'.