Simplification and Combining Terms: Master Algebraic Expressions and Like Terms

Section	Expression
First Leg	$x$
Second Leg	$3 x + 7$
Third Leg	$4 x - 6$

Section

Expression

First Leg

x

Second Leg

3 x + 7

Third Leg

4 x - 6

	Saturday's Visitors
	Children	Adults
Before Noon	$7$	$12$
After Noon	$12$	$20$

Saturday's Visitors

Children

Adults

Before Noon

7

12

After Noon

12

20

	Sunday's Visitors
	Children	Adults
Before Noon	$8$	$15$
After Noon	$3$	$4$

Sunday's Visitors

Children

Adults

Before Noon

8

15

After Noon

3

4

	Saturday's Visitors
	Children $($)$	Adults $($)$	Total $($)$
Before Noon	$7 x$	$12 x^{2}$	$7 x + 12 x^{2}$
After Noon	$12 y$	$20 y^{2}$	$12 y + 20 y^{2}$

Saturday's Visitors

Children

($)

Adults

($)

Total

($)

Before Noon

7 x

12 x^{2}

7 x + 12 x^{2}

After Noon

12 y

20 y^{2}

12 y + 20 y^{2}

	Sunday's Visitors
	Children $($)$	Adults $($)$	Total $($)$
Before Noon	$8 x$	$15 x^{2}$	$8 x + 15 x^{2}$
After Noon	$3 y$	$4 y^{2}$	$3 y + 4 y^{2}$

Sunday's Visitors

Children

($)

Adults

($)

Total

($)

Before Noon

8 x

15 x^{2}

8 x + 15 x^{2}

After Noon

3 y

4 y^{2}

3 y + 4 y^{2}

	Vases $($)$	Plush Toys $($)$	Paintings $($)$	Total $($)$
First Group	$3 a$	$4 b$	$5 c$	$3 a + 4 b + 5 c$
Second Group	$- 2 a$	$6 b$	$1 c$	$- 2 a + 6 b + 1 c$
Third Group	$1 a$	$0$	$- 1 c$	$1 a - 1 c$

Vases

($)

Plush Toys

($)

Paintings

($)

Total

($)

First Group

3 a

4 b

5 c

3 a + 4 b + 5 c

Second Group

- 2 a

6 b

1 c

- 2 a + 6 b + 1 c

Third Group

1 a

0

- 1 c

1 a - 1 c

Simplify the given expression.

x + 31 + 5 x - 2

We will begin by identifying the like terms to simplify the expression. Remember that only like terms — constant terms or terms with the same variable — can be combined. x + 31 + 5x - 2 In this case, we have two x-terms and two constants. Let's use the Commutative Property of Addition to rearrange the terms. Then we can combine them more easily.

Now the expression has one x-term and one constant. Since these terms cannot be combined further, the expression is simplified. We did it!

Simplify the given expression.

3.5 c^{2} + 8.5 + 14 c - 0.5 - 12 c - 13.5 c^{2}

We will begin by identifying the like terms to simplify the expression. Remember, only like terms — constant terms or terms with the same variable — can be combined. 3.5c^2 + 8.5 + 14c - 0.5 - 12c - 13.5c^2 In this case, we have two c^2-terms, two c-terms, and two constants. Let's use the Commutative Property of Addition to rearrange the terms. Then we can combine them more easily.

Now the expression has one c^2-term, one c-term, and one constant. Since these terms cannot be combined further, the expression is simplified. We did it!

Consider the following expressions.

Expression I : Expression II : 7 a + 10 - 3 a x a + 10

What value of

x

makes these expressions equivalent?

We want to know what value of x makes these expressions equivalent. Expression I: & 7a+10 -3a Expression II: & xa+10 Let's begin by simplifying Expression I. First, we will look for like terms — constant terms or terms with the same variable. Remember that only like terms can be combined. 7a + 10 - 3a We can see that there are two a-terms and one constant. Let's apply the Commutative Property of Addition to group these terms together and combine them.

Now let's compare these expressions. Expression I: & 4a+10 Expression II: & xa+10 We can see that if x has a value of 4, these expressions will be equivalent!

Consider the following expressions.

Expression I : Expression II : - 19 b + 7 + 21 b - 2 2 b + x

What value of

x

makes these expressions equivalent?

We want to know which value of x makes the given expressions equivalent. Expression I: & -19b+7+21b-2 Expression II: & 2b+x Let's start by identifying and grouping the like terms — constant terms or terms with the same variable. Remember that only these terms can be combined! -19b + 7 + 21b - 2 We can see that there are two b-terms and two constants. Let's apply the Commutative Property of Addition to group these terms together to combine them.

Now let's compare these expressions. Expression I: & 2b+ 5 Expression II: & 2b+ x We can see that the expressions will be equivalent if x has a value of 5. Therefore, 5 is the answer. We did it!

After school, Tiffaniqua and nine of her friends went to the bowling alley.

The alley is running a special that people can play for a price of

$ p .

However, Tiffaniqua and seven of her friends paid

$ 5

extra to rent shoes. Write and simplify an equation for the total amount that the group paid.

Tiffaniqua and nine friends went to the bowling alley. Eight members of the group paid $ p to play and an extra $ 5 to rent shoes. The remaining two friends only paid the $ p to play. We can find how much the friends paid as a whole paid by multiplying what each group paid by the number of people in that group.

	Games and Shoe Rental	Games Only
Price for One Person	p+5	p
Total	8(p+5)	2p

Now that we have the amount of money paid by both group, we can add them together to find the total price the friends paid. Let's write this as an expression. 8(p+5)+ 2p This expression represents the total amount of money paid by the friends, but now we need to simplify it. First, let's use the Distributive Property. Then we can combine like terms to finish the simplification.

The total amount paid by the friends is $10p + 40.

Simplify Algebraic Expressions

Catch-Up and Review

How Can These Terms Be Grouped?

Like Terms

Identifying Like Terms

Reducing the Number of Terms

Combining Like Terms

Heichi's Path to the Museum

Hint

Solution

Weekend Visitors to the Museum

Hint

Solution

A Curious Occurrence in the Souvenir Shop

Hint

Solution

Grouping Like Terms

Simplify Algebraic Expressions

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