2(x-5) + 6 ≥ 9x - 2(x-3) Distribute the 2 and -2: 2x - 10 + 6 ≥ 9x - 2x + 6 Combine like terms: 2x - 4 ≥ 7x + 6 Subtract 2x from both sides: -4 ≥ 5x + 6 Subtract 6 from both sides: -10 ≥ 5x Divide by 5 (since the coefficient of x is 5): -2 ≥ x
Therefore, the solution to the inequality 2(x-5) + 6 ≥ 9x - 2(x-3) is x ≤ -2.
Let's simplify the given inequality step by step:
2(x-5) + 6 ≥ 9x - 2(x-3)
Distribute the 2 and -2:
2x - 10 + 6 ≥ 9x - 2x + 6
Combine like terms:
2x - 4 ≥ 7x + 6
Subtract 2x from both sides:
-4 ≥ 5x + 6
Subtract 6 from both sides:
-10 ≥ 5x
Divide by 5 (since the coefficient of x is 5):
-2 ≥ x
Therefore, the solution to the inequality 2(x-5) + 6 ≥ 9x - 2(x-3) is x ≤ -2.