Question

Solve the inequality, if possible.
3(2 + x) >= 14 - 2x

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

OA. The solution is _. (Type an inequality. Simplify your answer.)
OB. The solution is all real numbers.
OC. There is no solution.

Answer 1

To solve the inequality, we can start by distributing 3 to both terms inside the parentheses:

6 + 3x ≥ 14 - 2x

Next, we can combine like terms by adding 2x to both sides:

6 + 5x ≥ 14

Subtracting 6 from both sides gives us:

5x ≥ 8

Finally, we divide both sides by 5 to solve for x:

x ≥ 8/5

Therefore, the solution to the inequality is:

OA. The solution is x ≥ 8/5.