Solve the following inequality and graph the solution set on a number line.
\[
22(x+1)-43< 21 x+1
\]
What is the solution set?
\[
\{x \mid \square \text { (Type an inequality.) }
\]
What is the graph of the solution set?
A.
B.
c.
D.
Answer
To graph the solution set, draw a number line and shade all numbers less than 22. The graph should have an open circle at 22 and the shading should extend to the left of 22.
Step 1 ：First, distribute the 22 in the left side of the inequality: \(22x + 22 - 43 < 21x + 1\).
Step 2 ：Simplify the left side of the inequality: \(22x - 21 < 21x + 1\).
Step 3 ：Subtract \(21x\) from both sides of the inequality: \(x - 21 < 1\).
Step 4 ：Add 21 to both sides of the inequality: \(x < 22\).
Step 5 ：The solution set is \(\{x \mid x < 22\}\).
Step 6 ：To graph the solution set, draw a number line and shade all numbers less than 22. The graph should have an open circle at 22 and the shading should extend to the left of 22.
