Answer:
[tex]x< \frac{45}{41}[/tex] or [tex]x< 1.098[/tex]
The graph in the attached figure
Step-by-step explanation:
we have
[tex]0.2x-2 < 7-8x[/tex]
Solve for x
Adds 2 both sides
[tex]0.2x-2+2 < 7-8x+2[/tex]
[tex]0.2x < 9-8x[/tex]
Adds 8x both sides
[tex]0.2x+8x < 9-8x+8x[/tex]
[tex]8.2x < 9[/tex]
Divide by 8.2 both sides
[tex]x < 9/8.2[/tex]
Remember that
[tex]8.2=82/10[/tex]
substitute
[tex]x < 9/(82/10)[/tex]
[tex]x< \frac{90}{82}[/tex]
Simplify
[tex]x< \frac{45}{41}[/tex] or [tex]x< 1.098[/tex]
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
