Question

Solve the compound inequality below and graph its solution on the number line

X +7<7 or 5 2x>7

Answer 1

The solution to the compound inequality "x + 7 < 7 or 10x > 7" is:

`\[ x < 0 \text{ or } x > (7)/(10) \]`

How to solve compound inequality?

For the first inequality:

x + 7 < 7

x < 0

For the second inequality (assuming the intended meaning is 10x > 7:

10x > 7

`\[ x > (7)/(10) \]`

The solution to the compound inequality "x + 7 < 7 or 10x > 7" is:

`\[ x < 0 \text{ or } x > (7)/(10) \]`

The green region on the left represents all x values less than 0, solving the inequality x + 7 < 7.

The magenta region on the right represents all x values greater than
`\( (7)/(10) \)`, solving the inequality 10x > 7. The dashed lines at x = 0 and
`\( x = (7)/(10) \)` indicate where the inequalities change from true to false.