Question

graph the solution to the following inequality: 38 - k < 5 - 2k

Explanation:

Step1: Add 2k to both sides

$38 - k+2k<5 - 2k+2k$
$38 + k<5$

Step2: Subtract 38 from both sides

$38 + k-38<5 - 38$
$k<-33$

To graph this on a number - line:

1. Draw a number line.
2. Mark a point at - 33.
3. Since $k < - 33$, draw an open circle at - 33 (because the inequality is strict, i.e., $k$ cannot equal - 33) and draw an arrow to the left of - 33 to represent all the values of $k$ that satisfy the inequality.

Answer:

The solution of the inequality is $k < - 33$. On a number - line, it is represented by an open circle at - 33 and an arrow pointing to the left.