3x−91>−87 OR 21x−17>25
Just work on each part independently, keeping the OR as is
3x−91>−87 OR 21x−17>25
3x > 4 OR 21x > 42
x > 4/3 OR x > 2
since the x > 2 is covered by the x > 4/3 and we have the UNION of the two relations
x > 4/3
Let's break down and solve each inequality step-by-step:
Inequality 1: 3x - 91 > -87
Step 1: Add 91 to both sides of the inequality:
3x - 91 + 91 > -87 + 91
3x > 4
Step 2: Divide both sides of the inequality by 3:
(3x)/3 > 4/3
x > 4/3
Inequality 2: 21x - 17 > 25
Step 1: Add 17 to both sides of the inequality:
21x - 17 + 17 > 25 + 17
21x > 42
Step 2: Divide both sides of the inequality by 21:
(21x)/21 > 42/21
x > 2
So, the solutions for the inequalities are:
For the first inequality: x > 4/3
For the second inequality: x > 2
To solve the inequalities 3x - 91 > -87 and 21x - 17 > 25, we need to isolate the variable x on each side of the inequality sign. Let's solve them step by step:
Inequality 1: 3x - 91 > -87
1. Add 91 to both sides of the inequality:
3x - 91 + 91 > -87 + 91
3x > 4
2. Divide both sides of the inequality by 3 (since 3 is the coefficient of x):
(3x)/3 > 4/3
x > 4/3
Inequality 2: 21x - 17 > 25
1. Add 17 to both sides of the inequality:
21x - 17 + 17 > 25 + 17
21x > 42
2. Divide both sides of the inequality by 21 (since 21 is the coefficient of x):
(21x)/21 > 42/21
x > 2
The solutions to the inequalities are:
For 3x - 91 > -87, x > 4/3
For 21x - 17 > 25, x > 2