1. Solving Equations with Variables on Both Sides
Lesson 4.7
Solving Equations with Variables on Both Sides

2. Warm-Up Solve each equation. Check your solution. –9x – 21 = 24 x = –5
–3m + (–7m) + 2m = –80
x = –5
y = 0.5
m = 10

3. Solving Equations with Variables on Both Sides
Lesson 4.7
Solving Equations with Variables on Both Sides
Simplify and solve equations with variables on both sides of the equation.

4. Solving Equations with Variables on Both Sides
Move one variable term to the opposite side of the equals sign using inverse operations.
Move all constants away from the variable using inverse operations.
Use division to isolate the variable.

5. Example 1
Solve the equation for the variable. Check the solution. a. 3x – 26 = 7x + 2 Write the equation. Subtract 3x from both sides. Subtract 2 from each side of the equation. Divide both sides by 4.  Check the solution.
3x – 26 = 7x + 2
– 3x – 3x a
– 26 = 4x + 2
– – 2
– 28 = 4x a a
– 7 = x a
3(–7) – 26 ≟ 7(–7) + 2
–21 – 26 ≟ –
– 47 = – 47

6. Example 1 Continued…
Solve the equation for the variable. Check the solution. b. 6m + 22 = – 2m + 10 Write the equation. Add 2m to both sides. Subtract 22 from each side. Divide both sides by 8.  Check the solution.
–2m is the same as subtracting 2m, so the inverse operation is adding 2m.
6m + 22 = – 2m + 10
+2m m a
8m = 10
a – –22
8m = –12
m = –1.5
6(–1.5) ≟ –2(–1.5) + 10
– ≟
13 = 13

7. Example 2
The Underwood family is 340 miles away from home and are headed toward home at a rate of 52 miles per hour. The Underwoods’ next-door neighbors, the Jacksons, are leaving home, traveling towards the Underwoods’ at a rate of 48 miles per hour. How long will it be before they pass each other?
Let h represent the number of hours the two families have been on the road.
The expression that represents the Underwoods’ distance from home is 340 – 52h. The expression that represents the Jacksons’ distance from home is 48h.
Set the two expressions equal to one another.
Add 52h to both sides.
Divide each side by 100.
The Jackson and Underwood families will pass each other after 3.4 hours.
340 – 52h = 48h
+52h h
340 = 100h
3.4 = h a

8. Communication Prompt
What do you think is most important to remember when solving equations?

9. Exit Problems Solve each equation. Check your solution.
8x + 12 = 3x + 37
–11 + p = 3p – 3
x = 5
p = – 4