Question

Graph the solution of the inequality on a number line.

2(x − 3) – 5x < x-2
Ο
Α.
OB.
OC
OD.
℗
-5 -4 -3 -2 -1 0 1 2
←
+1
-5 -4 -3 -2 -1 0 1
#2
0111
1
-5 -4 -3 -2 -1 0
2
3 4 5
3 4 5
3 4
+
5
4
110111
-5 -4 -3 -2 -1 0 1 2 3 4 5

Answer 1

Choice D : x > - 1

Explanation:

Left hand side (LHS) of the inequality can be siimplified

`2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\`

Inequality becomes

`-3x-6 < x-2`

Move x to the left side and -6 to the right side:

`-3x - x < -2 + 6\\\\-4x < 4\\\\`

Multiply both sides by -1(the inequality sign changes to >)

`4x > -4\\\\`

Divide both sides by 4:

`x > -1`

The number line corresponding to this is the fourth choice