1. Example 1A: Solving Inequalities with Variables on Both Sides
Solve the inequality and graph the solutions.
y ≤ 4y + 18
y ≤ 4y + 18
–y –y
0 ≤ 3y + 18
To collect the variable terms on one side, subtract y from both sides.
Since 18 is added to 3y, subtract 18 from both sides to undo the addition.
– – 18
–18 ≤ 3y
Since y is multiplied by 3, divide both sides by 3 to undo the multiplication.
–6 ≤ y (or y  –6)
–10 –8 –6 –4 –2 2 4 6 8 10

2. Example 1B: Solving Inequalities with Variables on Both Sides
Solve the inequality and graph the solutions.
4m – 3 < 2m + 6
To collect the variable terms on one side, subtract 2m from both sides.
–2m – 2m
2m – 3 <
Since 3 is subtracted from 2m, add 3 to both sides to undo the subtraction
2m <
Since m is multiplied by 2, divide both sides by 2 to undo the multiplication. 4 5 6

3. Lesson Quiz: Part III
Solve each inequality.
5. 2y – 2 ≥ 2(y + 7)
no solutions
6. 2(–6r – 5) < –3(4r + 2)
all real numbers