Question

Solve each of the given compound inequalities. Enter your answers using interval notation.

x−5<−4 and −7x+6≤−71

Answer 1

1.
`\:\left(-\infty \:,\:1\right)`
2.
`\:[11,\:\infty \:)`

Explanation:

Given the following questions:


`x-5 < -4`

`-7x+6\leq-71`

To find the answer we solve as if it is a two-step equation where we add/subtract on both sides.

Question one:

`x-5 < -4`

`-5+5=0`

`-4+5=1`

`x < 1`

`\:\left(-\infty \:,\:1\right)`

Question two:

`-7x+6\leq-71`

`6-6=0`

`-71+-6=-77`

`-7x\leq-77`

`-7x/-7=x`

`-77/-7=11`

`x\leq11`

`\:[11,\:\infty \:)`

Which means your answers are "(-∞, 1) and [11, ∞)."

Hope this helps.