Which answer gives all the values of x for which the inequality 3x+2≥9−4x is true?

Answer 1

To find the values of x for which the inequality is true, we need to isolate x on one side of the inequality.

Starting with the given inequality:
3x + 2 ≥ 9 - 4x

First, we can add 4x to both sides of the inequality to get rid of the variable on one side:
3x + 4x + 2 ≥ 9 - 4x + 4x

This simplifies to:
7x + 2 ≥ 9

Next, we can subtract 2 from both sides of the inequality:
7x + 2 - 2 ≥ 9 - 2

This simplifies to:
7x ≥ 7

Finally, we can divide both sides of the inequality by 7 to isolate x:
(7x)/7 ≥ 7/7

This simplifies to:
x ≥ 1

Therefore, all values of x greater than or equal to 1 satisfy the inequality 3x + 2 ≥ 9 - 4x.