Review 1.1-1.5

1.1 Variable Expressions1.2 Addition and Subtraction

1.3 Multiplication and Division1.4 Multi-step equations

1.5 Variables on Both Sides

1) Solve r + 16 = -7Think of this equation as a balance scale.

Whatever you do to one side has to be done to the other to keep it balanced!

- 16 -16 r = -23

-23 + 16 = -7

1) Solve r + 16 = -71. Subtract 16 from both

sides2. Simplify vertically3. Check your answer

by substituting your answer back into the problem

3) Solve 8 = m - 3

1. m = 52. m = 113. m = 244. m = 8/3

Answer Now

5) Solve. -x - (-2) = 1 -x + 2 = 1 - 2 - 2 -x = -1 -1 -1

x = 1 -(1) + 2 = 1

1. Eliminate the double sign2. Subtract 2 from both sides3. Simplify vertically4. We haven’t gotten x by

itself. It still has a negative sign in front.

5. Divide bot sides by -16. Check your answer

Solve -y – (-3) = 71. y = 102. y = 43. y = -104. y = -4

Answer Now

1) Solve -5t = 60 -5 -5

t = -12

-5(-12) = 60

1. Divide both sides by -52. Simplify

3. Check your answer

2) Solve 15 = 6n 6 6

n = 5/2

1. Divide both sides by 62. Simplify

3. Check your answer

3) Solve -3v = -1291. v = -1262. v = -433. v = 434. v = 126

Answer Now

4) Solve

4 · · 4

x = -48

1.Clear the fraction – multiply both sides by 4

2.Simplify3.Check your answer

248 14

(3/2) · = 18 · (3/2) x = 54/2

x = 27

1.Clear the fraction – multiply both sides by the

RECIPRICAL2.Simplify

3.Check your answer

5) Solve = 18

2( )27 183

7) Solve 4 87

b

1. b = -562. b = -143. b = 144. b = 56

Answer Now

1) Solve 2x - 1 = -3 + 1 + 1

2x = -2 2 2 x = -12(-1) - 1 = -3-2 – 1 = -3

1. Add 1 to both sides

2. Simplify3. Divide both sides

by 24. Simplify5. Check your

answer

+ 4 + 4

3 · · 3

x = 36

12 – 4 = 8

123x

2) Solve 4 83x

1. Add 4 to both sides

2. Simplify3. Clear the fraction -

Multiply both sides by 3

4. Simplify5. Check your

answer

36 4 83

3) Solve 3y – 1 = 8

73

1. y = 32. y = -3

3. y = 4. y = 7

3

Answer Now

3) Solve

d – 4 = 6 + 4 + 4 d = 10

1. Clear the fraction - Multiply both sides by 2

2. Simplify3. Add 4 to both

sides4. Simplify5. Check your

answer 10 4 32

4) Solve 1 63

d

1. d = -72. d = -193. d = -174. d = 17

Answer Now

5) Solve 3 27a

-3 -3

a = 35

1. Subtract 3 from both sides

2. Simplify3. Clear the fraction –

Multiply both sides by -7

4. Simplify5. Check your answer

57a

3 2357

3 5 2

6) Solve 5z + 16 = 51 1. z = -352. z = -73. z = 354. z = 7

Answer Now

- 1 - 1

5 · · 5 3x = 15 3 3 x = 5

7) Solve 3 1 45x

1. Subtract 1 from both sides

2. Simplify3. Clear the fraction -

Multiply both sides by 54. Simplify5. Divide both sides by 36. Simplify7. Check your answer

3 35x

3( ) 1 455

Key SkillsKeep it balanced!

Solve 6n + 17 = 5 + 4n– 4n – 4n

2n + 17 = 5– 17 – 17

2n = -12 ÷ 2 ÷ 2

Subtract 4n from each side of the equal sign.

Subtract 17 from each side of the equal sign.

Divide by 2

n = – 6

Do This TogetherKeep it balanced!

Solve 3x + 19 = 4 + 8x

x = 3

Subtract 3x from each side of the equal sign.– 3x – 3x

19 = 4 + 5x Subtract 4 from each side of the equal sign.

– 4 – 4

15 = 5xDivide by 5

÷ 5 ÷ 5

Try ThisKeep it balanced!

Solve – 3x – 9 = – 13 – 7x

x = – 1

Add 3x to each side of the equal sign.+ 7x + 7x

4x – 9 = – 13 Add 13 to each side of the equal sign.

+ 9 + 9

4x = – 4Divide by – 4

÷ 4 ÷ 4

Do this together

Solve 4b + 3 = 3b + 6

b = 3

Subtract 4b from each side of the equal sign.– 4b – 4b

3 = – b + 6 Subtract 6 from each side of the equal sign.– 6 – 6

– 3 = – bDivide by – 1

÷ – 1 ÷ – 1

Two special cases:

6(4 + y) - 3 = 4(y - 3) + 2y

24 + 6y - 3 = 4y - 12 + 2y

21 + 6y = 6y - 12 - 6y - 6y 21 = -12 Never true!21 ≠ -12 NO SOLUTION!

3(a + 1) - 5 = 3a - 2

3a + 3 - 5 = 3a - 2

3a - 2 = 3a - 2-3a -3a -2 = -2 Always true!INFINITE SOLUTIONS

Let’s try another!

3n + 1 = 7n - 5 -3n -3n 1 = 4n - 5 +5 +5 6 = 4n 4 4Reduce! 3 = n 2

Check:

3(1.5) + 1 =? 7(1.5) - 5

4.5 + 1 =? 10.5 - 5

5.5 = 5.5

Solve:Distribute first. 5 + 2y + 8 = 5y - 15 + 10

Next, combine like terms. 2y + 13 = 5y – 5

Now solve. (Subtract 2y.) 13 = 3y - 5 (Add 5.) 18 = 3y

(Divide by 3.) 6 = yy = 6

5 + 2(y + 4) = 5(y – 3) + 10

4)

3 - 2x = 4x - 6 3 = 6x - 6 9 = 6x

x = 3/2

38

14

x 12

x 34

Steps:•Multiply each term

by the least common denominator (8) to eliminate fractions.

•Solve for x.•Add 2x.•Add 6.

•Divide by 6.

(8)38

(8)14

x (8)12

x (8)34

Try a few on your own:

• 9x + 7 = 3x - 5

• 8 - 2(y + 1) = -3y + 1

• 8 - 1 z = 1 z - 7 2 4

• x = -2

• y = -5

• z = 20

1. -3

2.

3.

4. 3

What is the value of x if 3 - 4x = 18 + x?

13

13

Answer Now

4) Solve -7(x - 3) = -7-7x + 21 = -7

- 21 - 21-7x = -28 -7 -7 x = 4-7(4 - 3) = -7 -7(1) = -7

1. Distribute2. Subtract 21 from both

sides3. Simplify4. Divide both sides by -75. Simplify6. Check your answer

What is the value of x if 3(x + 4) = 2(x - 1)?

Answer Now

1. -142. -133. 134. 14

Special Case #1 6) 2x + 5 = 2x - 3

-2x -2x 5 = -3

This is never true!No solutions

1. Subtract 2x from both sides

2. Simplify

Special Case #2 7) 3(x + 1) - 5 = 3x - 2

3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2

-3x -3x -2 = -2

This is always true!Infinite solutions or

identity

1. Distribute2. Combine like terms3. Subtract 3x from both

sides4. Simplify

What is the value of x if -3 + 12x = 12x - 3?

1. 02. 43. No solutions4. Infinite solutions

Answer Now

Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2?

Answer Now

1. -82. -23. 24. 8