1. Learning Target
Students will be able to: Solve inequalities that contain variable terms on both sides.

2. Solve the inequality and graph the solutions. y ≤ 4y + 18
–10 –8 –6 –4 –2 2 4 6 8 10
4m – 3 < 2m + 6 4 5 6

3. Solve the inequality and graph the solutions.
4x ≥ 7x + 6
–10 –8 –6 –4 –2 2 4 6 8 10

4. The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding. How many windows must a house have to make the total cost from The Home Cleaning Company less expensive than Power Clean?
13 < w
The Home Cleaning Company is less expensive for houses with more than 13 windows.

5. Solve the inequality and graph the solutions.
2(k – 3) > 6 + 3k – 3
–12 –9 –6 –3 3

6. 0.9y ≥ 0.4y – 0.5 Solve the inequality and graph the solution. –5 –4–3 –2 –1 1 2 3 4 5

7. Solve the inequality and graph the solutions.
0.5x – x < 0.3x + 6 –5 –4 –3 –2 –1 1 2 3 4 5

8. There are special cases of inequalities called identities and contradictions.

10. Solve the inequality.
2x – 7 ≤ 5 + 2x
The inequality 2x − 7 ≤ 5 + 2x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions.

11. No values of y make the inequality true. There are no solutions.
Solve the inequality.
2(3y – 2) – 4 ≥ 3(2y + 7)
No values of y make the inequality true. There are no solutions.
HW pp /20-38,40-48even,49-51,56-66,73-76 

12. Warm Up Solve each equation. 1. 2x = 7x + 15 2. x = –3
3y – 21 = 4 – 2y
y = 5
3. 2(3z + 1) = –2(z + 3)
z = –1
4. 3(p – 1) = 3p + 2
no solution
5. Solve and graph 5(2 – b) > 52.
b < –3 –5 –3 –2 –1 –4 –6