1. Objectives The student will be able to:
Solve two-step equations
Solve equations with variables on both sides
Solve equations containing grouping symbols.
Adapted from original designed by Skip Tyler, Varina High School

2. + - ÷ • Solve: 8x + 5 = 61 Step 1 Step 2
Completely UNDO those steps Working in reverse order using inverse operations!
Examine the problem
Figure out the order that you would DO to solve if you knew the value of the variable.
Use PEMDAS! + - ÷ •

3. Solve: 8x + 5 = 61 – 5 – 5 8x = 56 x = 7 8(7) + 5 = 61 8 56 + 5 = 61
– 5 – 5
8x = 56
x = 7
8(7) + 5 = 61
= 61
Draw “the river”
Subtract 5 from both sides
Simplify
Divide both sides by 8
Check your answer 8

4. Find the value of z if 7z + 5 = 40
245 5 9
315
Answer Now

5. Solve: + 9 + 9 = 40 −4   −4 a = −160 40 − 9 = 31 Draw “the river”
= 40
a = −160
40 − 9 = 31
Draw “the river”
Add 9 to both sides
Simplify
Multiply both sides by -4
Check your answer
−4   −4

6. Solve: − 8 − 8 = − 20 4   4 y = −80 −20 + 8 = −12 Draw “the river”
Subtract 8 from both sides
Simplify
Multiply both sides by 4
Check your answer
− 8 − 8
= − 20
y = −80
− = −12
4   4

7. Find the value of z if 30 4
100
1.2
Answer Now

8. Solve: = (4)3 m – 8 = 12 + 8 = + 8 m = 20 12/3 = 4 Draw “the river”
Multiply both sides by 3
Simplify
Add 8 to both sides
Check your answer
= (4)3
m – 8 = 12
+ 8 = + 8
m = 20
12/3 = 4

9. Find the value of z if
186 51 39
174
Answer Now

10. Solve: 3x + 2 = 4x – 1
You need to get the variables on one side of the equation.
It does not matter which variable you move.
Try to move the one that will keep your variable positive.

11. Solve: 3x + 2 = 4x – 1 - 3x - 3x 2 = x – 1 + 1 + 1 3 = x
3 = x
3(3) + 2 = 4(3) – 1
9 + 2 = 12 – 1
Draw “the river”
Subtract 3x from both sides
Simplify
Add 1 to both sides
Check your answer

12. Solve: 8y – 9 = –3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11
11y =
y = 1
8(1) – 9 = –3(1) + 2
Draw “the river”
Add 3y to both sides
Simplify
Add 9 to both sides
Divide both sides by 11
Check your answer

13. What is the value of x if 3 – 4x = 18 + x?
– 3 3
Answer Now

14. Solve: 4 = 7x – 3x 4 = 4x 4 4 1 = x 4 = 7(1) – 3(1) Draw “the river”
1 = x
4 = 7(1) – 3(1)
Draw “the river”
– Notice the variables are on the same side!
Combine like terms
Divide both sides by 4
Simplify
Check your answer

15. Solve: – 7(x – 3) = – 7 – 7x + 21 = – 7 – 21 – 21 – 7x = – 28 – 7 – 7
– – 21
– 7x = – 28
– – 7
x = 4
– 7(4 – 3) = – 7
– 7(1) = – 7
Draw “the river”
Distribute
Subtract 21 from both sides
Simplify
Divide both sides by -7
Check your answer

16. What is the value of x if 3(x + 4) = 2(x – 1)?
-14
-13 13 14
Answer Now

17. Solve: 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6
Draw “the river”
Clear the fraction – multiply each term by the LCD
Simplify
Add 2x to both sides
Add 6 to both sides
Divide both sides by 6
Check your answer
3 - 2x = 4x – 6
+ 2x +2x
= 6x – 6
= 6x
or 1.5 = x

18. – 2x – 2x 5 = – 3 This is never true! No solutions
Special Case # ) 2x + 5 = 2x – 3
– 2x – 2x
5 = – 3
Draw “the river”
Subtract 2x from both sides
Simplify
This is never true!
No solutions

19. Infinite solutions or identity
Special Case # (x + 1) – 5 = 3x – 2
3x + 3 – 5 = 3x – 2
3x – 2 = 3x – 2
– 3x – 3x
– 2 = – 2
Draw “the river”
Distribute
Combine like terms
Subtract 3x from both sides
Simplify
This is always true!
Infinite solutions or identity

20. What is the value of x if – 3 + 12x = 12x – 3?4
No solutions
Infinite solutions
Answer Now

21. Challenge! What is the value of x if – 8(x + 1) + 3(x – 2) = – 3x + 2?-8 -2 2 8
Answer Now