Please help!
What is the solution of 5 - 2x is greater than -3 OR -3x + 9 is less than -6
Thank you
5 - 2x ≥ -3 OR -3x + 9 ≤ -6
-2x ≥ -8 or -3x ≤ -15
x ≤ 4 OR x ≥ 5
I appreciate the explanation-I get it now
To find the solution to the given equation, we need to solve each inequality separately and then combine the solutions.
1) 5 - 2x > -3
To solve this inequality, we need to isolate the variable x. Let's solve it step by step:
a) Subtract 5 from both sides: -2x > -3 - 5
Simplifying, we have: -2x > -8
b) Divide both sides by -2. Remember, when dividing or multiplying by a negative number, we need to reverse the inequality sign:
x < -8 / -2
Simplifying, we have: x < 4
So the first inequality has the solution: x < 4
2) -3x + 9 < -6
To solve this inequality, we will follow a similar process:
a) Subtract 9 from both sides: -3x < -6 - 9
Simplifying, we have: -3x < -15
b) Divide both sides by -3, reversing the inequality sign:
x > -15 / -3
Simplifying, we have: x > 5
So the second inequality has the solution: x > 5
Now, to find the combined solution, we take the union of the individual solutions. In other words, any values of x that satisfy either inequality will be part of the solution.
The combined solution is: x < 4 OR x > 5
This means any value of x that is less than 4 or greater than 5 will make either one of the inequalities true.