solv the inequality:
1. 7-3x [is less than or equal to] 22
---> x [is greater than or equal to] -5
2. 4x-2/3 [is greater than or equal to] 1/3
---> x [is greater than or equal to] 3/5
are these correct??
To solve the inequalities you provided, here are the steps:
1. 7 - 3x ≤ 22
To solve this inequality, you want to isolate the variable x. Begin by subtracting 7 from both sides of the inequality:
7 - 7 - 3x ≤ 22 - 7
-3x ≤ 15
Next, divide both sides of the inequality by -3. When dividing by a negative number, the direction of the inequality sign must be flipped:
(-3x) / -3 ≥ 15 / (-3)
x ≥ -5
Therefore, the solution to this inequality is x ≥ -5.
2. 4x - 2/3 ≥ 1/3
To solve this inequality, again you want to isolate the variable x. Begin by adding 2/3 to both sides of the inequality:
4x - 2/3 + 2/3 ≥ 1/3 + 2/3
4x ≥ 3/3
Simplify the right side of the inequality:
4x ≥ 1
Finally, divide both sides of the inequality by 4:
(4x) / 4 ≥ 1 / 4
x ≥ 1/4
Therefore, the solution to this inequality is x ≥ 1/4.
So, your solutions are correct.