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.
1. Let's start by expanding out first.
\(-4(x+4) > x+ 7 = -4x-16 >x+7\)
Adding 4x on both sides and subtracting 7, we get:
Dividing by 5, we get:
That gives us an interval of:
2. Similar to the last problem, let's just first add like terms to get a constraint on x.
\(2x-5\leq -x + 12\)
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!)