Question

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

Answer 1

Answer:

$x< \frac{45}{41}$  or $x< 1.098$

The graph in the attached figure

Step-by-step 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

$x < 9/(82/10)$

$x< \frac{90}{82}$

Simplify

$x< \frac{45}{41}$  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