This document provides examples of solving multi-step equations and inequalities. It includes sample problems worked out step-by-step with explanations and videos. Readers are prompted to try similar problems on their own. Application problems involve equations modeling scenarios such as mountain climbers meeting at a certain point and boys reaching the same wrestling weight after losing or gaining weight over time.

1. Solving with variables
on both sides.
4.4 and 4.5

2. Review:
Watch this short video and
do the steps as you watch.
x + 7(x + 1) = 87
8x – 19 = 3x + 31

3. New:
Watch this short video and
do the steps as you watch.
3x + 10 = 4x + 5

4. Now you try it! Do your best. 
1.
5y + .6 =
-3y – 4.4
2.
1n + 33 = 5 – 1n
6
Plug your answer back in to check!

5. Watch this short video and
do the steps as you watch.
3(x – 1) = 2(x + 7) + 2

6. Watch this short video and
do the steps as you watch.
5 – 2(x + 2) = 3 – (x – 3)

7. Now you try it!

3. -3(a + 14) = 6(2a + 3)
4. 7(8x – 3) + 2x = 72 – 4x

8. 5.
A mountain climber is injured. His partner radios
for help, then they begin to descend from their height
of 12,500 ft. at a speed of about 200 feet per hour.
The rescue team starts at an altitude of 6,500 feet and
climbs 1,000 feet per hour.
a. Define the variable. X = hours
Write an equation for when they will meet.
Injured = 12500 – 200x
Rescue = 6500 + 1000x
12500 – 200x = 6500 + 1000x

9. X = hours
12, 500 – 200x = 6,500 + 1000x
b. How long does it take for them to meet?
c. At what height do they meet?
(Go back and plug in.)

10. Raul and Tom both with to wrestle at the same
weight. Raul, who weighs 148 pounds, plans to
gain a pound a week. Tom weighs 166 pounds
plans to lose 2 lbs. a week.
a. Define the variable. X = weeks
Write an equation for when they will be the
same weight.
R = 148 + 1x
and
T = 166 – 2x
148 + x = 166 – 2x

11. 148 + x = 166 – 2x
b. How long will it take the boys to reach
the same weight?
c. At what common weight will the boys
wrestle?

12. Inequalities: Solve as usual
7. 8w < 10w – 30
8.
12x + 3 + 4x
2(7x + 1)

13. 9. Nine times a number is less than the
sum of 5 times that number and 13.
Find the number.
9n < 5n + 13
NOTE:
“5 times the sum of a number and 13”
implies the distributive property.
5(n + 13)

14. Homework:
4-4 # 1, 3, 5, 7, 9
4-5 #1, 7, 9, 10, 19, 20
Quiz – Next Tuesday