Which answer gives all the values of x
for which the inequality 3x+2≥9−4x
is true?
x≥1
x greater-than-or-equal-to 1
x=1
x equals 1
x≤1
x less-than-or-equal-to 1
x>1
x greater than 1
The answer that gives all the values of x for which the inequality is true is:
x≥1
x greater-than-or-equal-to 1
To solve the inequality 3x + 2 ≥ 9 - 4x, we need to isolate the variable x. Following the steps:
1. Combine like terms by adding 4x to both sides of the inequality:
3x + 4x + 2 ≥ 9 - 4x + 4x
7x + 2 ≥ 9
2. Subtract 2 from both sides of the inequality:
7x + 2 - 2 ≥ 9 - 2
7x ≥ 7
3. Divide both sides of the inequality by 7 to solve for x:
(7x) / 7 ≥ 7 / 7
x ≥ 1
Therefore, the values of x for which the inequality 3x + 2 ≥ 9 - 4x is true are:
- x ≥ 1
- x greater-than-or-equal-to 1