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.

Guest Mar 21, 2020

#1**+1 **

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!)

jfan17 Mar 21, 2020