−25x+175>225 AND5x−83≥−73
there are actually no solutions i just did this on khan academy
no solution
To solve the inequalities −25x + 175 > 225 and 5x − 83 ≥ −73, we need to isolate the variable x.
Let's solve the first inequality, −25x + 175 > 225:
Step 1: Subtract 175 from both sides of the inequality:
−25x + 175 - 175 > 225 - 175
−25x > 50
Step 2: Divide both sides of the inequality by -25. Remember that when dividing or multiplying by a negative number, we need to flip the direction of the inequality:
−25x / -25 < 50 / -25
x < -2
So the solution to the first inequality is x < -2.
Now, let's solve the second inequality, 5x − 83 ≥ −73:
Step 1: Add 83 to both sides of the inequality:
5x − 83 + 83 ≥ −73 + 83
5x ≥ 10
Step 2: Divide both sides of the inequality by 5:
(5x) / 5 ≥ 10 / 5
x ≥ 2
So the solution to the second inequality is x ≥ 2.
In summary, the solution to the system of inequalities −25x + 175 > 225 and 5x − 83 ≥ −73 is x < -2 or x ≥ 2.
-25 x > 50
25 x < -50
x < -2
and
5 x ≥ 10
x ≥ 2
nothing lies both to the left of -2 and to the right of +2