Simplifying Linear Expressions

Simplifying Expressions

Multiple Choice

4a + 9 + a

• 5a + 9
• 14a
• 3a + 9
• 5a - 9

4a + 9 + a

• WHAT ARE THE LIKE TERMS?

• 4a and a are like terms. We can add them.

• When we add 4a + a, we get 5a

• We can't add 5a + 9 because they are NOT like terms.

Multiple Choice

Simplify:6b + 7b - 10

• 3b
• 13b - 10
• 13b² - 10
• 3b²

6b + 7b - 10

• The. like terms are 6b + 7b

• 6b + 7b = 13b

• You can't subtract 13b-10 becuase they are not like terms.

Multiple Choice

What is the simplified form of this expression
3x+4+5x+3

• 15x
• 8x+7
• 7x+8

3X + 4 + 5X + 3

• LIKE TERMS: 3X + 5X = 8X

• LIKE TERMS: 4+3=7

• You can't add 8X and 7 because they are not like terms

• Final answer: 8X + 7

Multiple Choice

Simplify the Expression. 
9z  - 21 - 3z + 10

• Simplified
• 9z - 21 - 7
• 9z - 11 -3z
• 6z - 11

9Z - 21 - 3Z + 10

• LIKE TERMS: 9Z -3Z = 6Z

• LIKE TERMS: -21 + 10 = -11

• You can't combine 6Z - 11 because they are not like terms

• FINAL ANSWER: 6Z - 11

Multiple Choice

Simplify:

5x - 6x - 8x + 7

• -9x + 7

• 10x + 7

• 9x + 7

• 9x - 7

5X - 6X - 8X + 7

• LIKE TERMS: 5X - 6X - 8X. This is a tricky one.

• 5X - 6X = -1X, or just -X.

• -X - 8X = -9X.

5X - 6X - 8X (See image)

• Start at 5. Go 6 to the left, you end up at -1

• From -1, go 8 more to the left. You end up at -9

• Therefore: 5X - 6X - 8X = -9X

-9x+7

• You can't combine -9X + 7 because

• That's right. They are not

• LIKE TERMS!

Multiple Choice

3 - 2a + 3a + 5a

• 5a+3
• 5a-3
• 6a + 3
• 8a+3

Multiple Choice

Simplify    5(2 - 7n) =

•  52 - 57n
• 10 - 7n
• 10 - 35n
• 10 + 35n

5(2 - 7n). Using distributive property

• MULTIPLY both terms by 5

• 5(2) = 10

• 5(-7n) = -35n

• You can't combine 10-35n because they are not LIKE TERMS

• Final answer: 10-35n

Multiple Choice

Simplify the expression: 7+3(1 - 2x) 

• 21 - 6x
• 10 - 2x
• 10 - 20x
• 10 - 6x

7 + 3(1-2X). BREAK IT DOWN!

• FIrst, let us use the distributive property. 3(1-2X)

• 3(1) = 3

• 3(-2X) = -6X

• YOU CAN'T COMBINE 3-6Xb because they are not like terms.

• So now we have 7 + 3 - 6X

• (TO BE CONTINUED)

7 + 3 - 6X

• OUR LIKE TERMS: 7+3=10

• You can't combine 10-6X because they are not like terms. So we could stop here if we want.

• Or: We could factor out a 2.

• 10-6X = 2(5-3X)

Multiple Choice

Simplify the expression:
6 + 2(7x - 3) 

• 12 + 7x
• 14x
• 14x + 3
• 9 + 7x

Multiple Choice

4(x+3) - 5

• 4x + 7

• 4x - 2

• 4x - 17

• 4x + 2

Multiple Choice

6(7 + x) + 5x

• 6x + 13

• x + 42

• 6x + 42

• 11x + 42

Multiple Choice

3(5 + 3x) - 4x

• -x + 8

• 7x + 15

• 5x + 15

• 7x + 8

Multiple Choice

5(y + 6) + 4

• 5y + 15

• 5y + 34

• 5y + 10

• y + 34

Multiple Choice

-5(y - 6) + 4

• -5y + 34

• 5y - 26

• -5y - 26

• 5y + 34

Multiple Choice

6x + 3(-2 - x) - 4

• 9x - 10

• 3x + 2

• 3x - 10

• 9x + 10

Multiple Choice

Simplify the expression:
6 + 2(7x - 3) 

• 12 + 7x
• 14x
• 14x + 3
• 9 + 7x

Multiple Choice

Simplify the expression: 7+3(1 - 2x) 

• 21 - 6x
• 10 - 2x
• 10 - 20x
• 10 - 6x

Multiple Choice

Simplify the expression: 7+3(1 - 2x) 

• 21 - 6x
• 10 - 2x
• 10 - 20x
• 10 - 6x

Multiple Choice

Simplify the expression:
6 + 2(7x - 3) 

• 12 + 7x
• 14x
• 8x + 6
• 9 + 7x

Multiple Choice

3(2x+1)+2(x-4)

• 8x-3
• 8x+11
• 4x-5
• 8x-5