Hi, there--
THE PROBLEM:
Solve the inequality. Then graph your solution.
10 < -2x OR 2x ≥ 0
A SOLUTION:
This inequality has two branches (on either side of the "OR.") Start with the left branch.
Divide both sides by -2 to isolate x on the right side. When we divide the terms of an
inequality by a negative number, we must reverse the direction of the inequality.
10 < -2x
-5 > x
Rewrite with x on the left side. If -5 is less than x, then x is greater than -5.
x < -5
Simplify the right branch.
2x ≥ 0
Divide both sides by 2 to isolate x on the left side.
x ≥ 0
We have x < -5 OR x ≥ 0
The numbers that satisfy this inequality are less than -5 OR greater than equal to 0.
THE GRAPH:are to the right of this circle.
x < -5 :: Draw a number line. Draw an open circle at -5. The numbers less than -5 are to the
left of this circle, so shade in a thick, solid arrow pointed to the left of -5.
x ≥ 0 :: Draw in a solid circle at 0. The numbers greater than 0 are to the right of this
circle, so shade in a thick, solid arrow pointed to the right of 0.
Hope this helps! Feel free to email if you have any questions about the solution.
Good luck with your math,
Mrs. F
math.in.the.vortex@gmail.com
