Question

How do you solve the inequality `8x-10> 7x+20`?

Answer 1

`" "`
Inequality Solution: `color(blue)(x>30`

Interval Notation: `color(blue)((30, oo)`

Explanation:

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Given inequality: `color(red)(8x-10>7x+20`

`color(green)("Step 1:"`

Simplify:

`8x-10>7x+20`

Subtract `color(red)(7x` from both sides of the inequality

`8x-10-color(red)(7x)>7x+20-color(red)(7x)`

`8x-10-color(red)(7x)>cancel(7x)+20-color(red)(cancel(7x))`

`8x-10-7x>20`

`x-10> 20`

`color(green)("Step 2:"`

`x-10> 20`

Add `color(red)(10` to both sides of the inequality

`x-10+color(red)(10)> 20+color(red)(10)`

`x-cancel 10+color(red)(cancel 10)> 20+color(red)(10)`

`color(blue)(x>30`

This is the final solution.

`color(green)("Step 3:"`

Verify the solution `color(red)(x>30` by graphing the inequality:

The shaded region indicates the solution area.

The dashed-line is the boundary line because points on the line don’t satisfy the inequality.

Hope it helps.