Answer: Read below.
Step-by-step explanation:
[tex]3x+17<47\\-6x+9<25[/tex]
Let's take the first one.
[tex]3x+17<47[/tex]
Subtract 17
[tex]3x<47-17\\3x<30[/tex]
Divide by 3
[tex]x<\frac{30}{3}\\ x<10[/tex]
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Now the second one.
[tex]-6x+9<25\\-6x<25-9\\-6x<16[/tex]
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.
[tex]x>\frac{16}{-6}[/tex]
[tex]x>-\frac{8}{3}[/tex]
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x has to be less than 10
x has to be greater than [tex]-\frac{8}{3}[/tex] or -2.66 approximately.
in the number line, make a hollow circle on [tex]-\frac{8}{3}[/tex] and draw an arrow up to [tex]10[/tex] where, again, you have to make a hollow circle. The circles have to be hollow because neither [tex]-\frac{8}{3}[/tex] nor 10 are part of the answers.
