Question

Solve the inequality. −2x+3>x−18 Enter the exact answer in interval notation.

Answer 1

Step 1

Given;

$-2x+3>x-18$

Required; To solve the inequality

Step 2

Bring like terms together

$-2x-x>-18-3$

Step 3

Simplify

$-3x>-21$

Step 4

Multiply both sides by -1

$-3x(-1)<-21(-1)_{}$

Step 5

Simplify

$3x<21$

Step 6

Divide by 3 and get the answer

$\begin{gathered} \frac{3x}{3}<\frac{21}{3} \\ x<7 \\ In\text{ in}terval\text{ notation;} \\ (-\infty,7) \end{gathered}$

Hence, the exact answer in interval notation is;

(-∞,7)