Question

solve the following inequality.
x - 5 < -7

1. write the answer as an interval, use \oo\ (two lower case os) for ∞.
2. graph the solution set.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
clear all draw:

Explanation:

Step1: Isolate the variable x

Add 5 to both sides of the inequality $x - 5 < - 7$. So $x-5 + 5< - 7+5$.

Step2: Simplify the inequality

We get $x < - 2$.

Step3: Write the answer in interval - notation

The interval - notation for $x < - 2$ is $(-\infty,-2)$.

Step4: Graph the solution set

On the number - line, we use an open circle at $x=-2$ (because $x$ is strictly less than $-2$) and draw an arrow to the left to represent all the values less than $-2$.

Answer:

1. $(-\infty,-2)$
2. On the number - line, place an open circle at $-2$ and draw an arrow to the left.