−25x+175>225 AND5x−83≥−73
−25x+175 > 225
x - 7 < -9
x < -2
5x−83 ≥ −73
5x ≥ 10
x ≥ 2
there is no number both less than -2 AND greater than 2
To solve the inequality −25x + 175 > 225, you need to isolate the variable x:
−25x + 175 > 225
Subtract 175 from both sides of the inequality:
−25x > 50
Next, divide both sides of the inequality by -25. Remember that when dividing by a negative number, the inequality sign flips:
x < -50/25
Simplifying the expression gives:
x < -2
To solve the inequality 5x − 83 ≥ -73, you need to isolate the variable x:
5x − 83 ≥ -73
Add 83 to both sides of the inequality:
5x ≥ 10
Next, divide both sides of the inequality by 5:
x ≥ 10/5
Simplifying the expression gives:
x ≥ 2
Therefore, the solution to the given system of inequalities is x < -2 and x ≥ 2.