4x-10<-5 ,x-2>4

Question

solve and graph the compound inequility.

Answer 1

Given inequalities are 4x - 10 < -5 and x - 2 > 4

1) Draw the coordinate plane.

Now first inequality 4x - 10 < -5.

2) Graph the line 4x - 10 = -5

3) Since the inequality symbol is < the boundary is not included the solution set.

Graph the boundary of the inequality 4x - 10 < -5 with dotted line.

4) To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality

-10 < -5

The statement is true.

5) Since the statement is true , shade the region contain point (0,0)

Shaded in fuchsia colour.

Now second inequality x - 2 > 4.

6) Graph the line x - 2 = 4

7) Since the inequality symbol is > the boundary is not included the solution set.

Graph the boundary of the inequality x - 2 > 4 with dotted line.

8) To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality

-2 > 4

The statement is false.

9)Since the statement is false , shade the region except contain point (0,0).

shaded in aqua colour.

Graph :

From the graph we can observe no intersecting points.

In this case there is no solution.

Answer 2

The compound inequality is 4x -10 < -5, x - 2 > 4

First inequality 4x - 10 < -5

4x  < -5+10

4x  < 5

x  < 5/4

x < 1.25

Second inequality x -2 > 4

x > 6

Solution x  < 1.25 or x  > 6

Graph