Question

Solve the inequality and show your solution on a number line: 0.2x−2<7−8x

Answer 1

`x< (45)/(41)` or
`x< 1.098`

The graph in the attached figure

Explanation:

we have

`0.2x-2 < 7-8x`

Solve for x

Adds 2 both sides

`0.2x-2+2 < 7-8x+2`

`0.2x < 9-8x`

Adds 8x both sides

`0.2x+8x < 9-8x+8x`

`8.2x < 9`

Divide by 8.2 both sides

`x < 9/8.2`

Remember that

`8.2=82/10`

substitute

`x < 9/(82/10)`

`x< (90)/(82)`

Simplify

`x< (45)/(41)` or
`x< 1.098`

The solution is the interval ------> (-∞, 45/41)

All real numbers less than 45/41

In a number line , the solution is the shaded area at left of x=45/41 (open circle)

The graph in the attached figure