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1. Solve the inequality -4(x+4)>x+7 Give your answer as an interval.

 

2. Solve the inequality 2x - 5 \(\le\) -x +12 Give your answer as an interval.

 Mar 21, 2020
 #1
avatar+402 
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Hey guest!

 

1. Let's start by expanding out first.

We get:

\(-4(x+4) > x+ 7 = -4x-16 >x+7\)

Adding 4x on both sides and subtracting 7, we get:

 

\(-23>5x\)

Dividing by 5, we get:

\(-23/5>x\)

That gives us an interval of:

\((-\infty,-23/5)\)

 

2. Similar to the last problem, let's just first add like terms to get a constraint on x.

We're given:

\(2x-5\leq -x + 12\)

Adding 5 and x on both sides, we get:

\(3x \leq 17\)

Dividing by 3 on both sides, we get:

\(x \leq 17/3\)

This gives us the interval of:

\((-\infty,17/3]\) with a square bracket on 17/3 to indicate its inclusion in the interval(remember, round parentheses are exclusive!)

 Mar 21, 2020
 #2
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Thank you very much!!! You are very good at this!!!!

 Mar 21, 2020
 #3
avatar+402 
+1

any time!

 Mar 21, 2020

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