Which graph below bests represent the solution set for - 2x + 5 + x < 3x + 13?
The equation we are given is -2x + 5 + x < 3x + 13. To represent the solution graphically, we need to simplify the equation and plot it on a graph.
First, let's simplify the inequality:
-2x + 5 + x < 3x + 13
-x + 5 < 3x + 13
-x - 3x < 13 - 5
-4x < 8
Dividing both sides of the inequality by -4, we get:
x > -2
This means that the solution set is all values of x greater than -2. We represent this graphically as an open circle on the number line at -2, with an arrow pointing to the right to indicate that the solution set includes all values greater than -2.
Here is a graph that best represents the solution set for the given inequality:
~>---|----|----|----|--->
-3 -2 -1 0 1
The open circle at -2 and the arrow to the right indicate that all values greater than -2 are part of the solution set.