Question

Solve the inequality 3(x - 2) + 1 ≤ 2x + 2(x + 2).

a) x < -5
b) x > -5
c) No solution
d) All real numbers

Answer 1

To solve the inequality 3(x - 2) + 1 ≤ 2x + 2(x + 2), distribute and combine like terms, isolate the x variable, and solve for x. The solution is x ≥ -9.

Step-by-step explanation:

To solve the inequality 3(x - 2) + 1 ≤ 2x + 2(x + 2), we will start by simplifying both sides of the equation.

1. Distribute the 3 and 2 to their respective terms: 3x - 6 + 1 ≤ 2x + 2x + 4
2. Combine like terms: 3x - 5 ≤ 4x + 4
3. Subtract 3x from both sides to isolate the x variable: -5 ≤ x + 4
4. Subtract 4 from both sides to get x alone: -9 ≤ x

The solution to the inequality is x ≥ -9, which means that the values of x that make the inequality true are equal to or greater than -9.