Question

3x+17<47
-6x+9<25
Solve the inequalities and make a number line

Answer 1

Answer: Read below.

Explanation:

`3x+17<47\\-6x+9<25`

Let's take the first one.

`3x+17<47`

Subtract 17

`3x<47-17\\3x<30`

Divide by 3

`x<(30)/(3)\\ x<10`

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Now the second one.

`-6x+9<25\\-6x<25-9\\-6x<16`

Here's the trick. You need to divide by -6; however, there's a rule. When you multiply or divide by negative numbers, the inequality sign flips.

`x>(16)/(-6)`

`x>-(8)/(3)`

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x has to be less than 10

x has to be greater than
`-(8)/(3)` or -2.66 approximately.

in the number line, make a hollow circle on
`-(8)/(3)` and draw an arrow up to
`10` where, again, you have to make a hollow circle. The circles have to be hollow because neither
`-(8)/(3)` nor 10 are part of the answers.