Expressions and Equations Review

Expressions and Equations Review

By Harley Pospical

Multiple Choice

Which one includes an equal sign?

• Expression

• Equation

• mathematical sentence

• includes variables, numbers, and operators

• DOES include an equal sign

• variables can only be one number

Equations

• mathematical phrase

• includes variables, numbers, and operators

• DOES NOT include an equal sign

• variables can be any number

Expressions

What are Expressions and Equations?

Match

Match the following parts of the equation below to their correct name

$$4+15x=60$$

• 15

• 4

• 15x

• +

• x

Coefficient

Constant

Term

Operator

Variable

• Coefficient

• Constant

• Term

• Operator

• Variable

COEFFICIENT--the number multiplying or dividing with your variable
CONSTANT--the number being added or subtracted to your variable
TERM--a constant or a variable and it's coefficient

PARTS OF AN EQUATION

Multiple Choice

Which part of the equation below is the COEFFICIENT

$$\frac{2}{3}x-24=72$$

• $$\frac{2}{3}x$$

• x

• 24

• -24

• $$\frac{2}{3}$$

Multiple Choice

Which part of the equation below is the CONSTANT

$$\frac{2}{3}x-24=72$$

• $$\frac{2}{3}x$$

• 72

• 24

• -24

• $$\frac{2}{3}$$

Fill in the Blanks

Like terms must have the same

and the same exponent.

Multiple Choice

Are the terms below LIKE or UNLIKE?

$$-15\ \ and\ \ -15x$$

• LIKE

• UNLIKE

Multiple Choice

Are the terms below LIKE or UNLIKE?

$$10m\ \ and\ \ 10m^2$$

• LIKE

• UNLIKE

Multiple Choice

Are the terms below LIKE or UNLIKE?

$$\frac{1}{4}c\ \ and\ \ -9c$$

• LIKE

• UNLIKE

Open Ended

Give an example of a like term for the term below:

$$14y$$

Open Ended

Give an example of a like term for the term below:

$$-23xy$$

Open Ended

Give an example of a like term for the term below:

$$200$$

ONLY combine terms that have the same variable
PAY CLOSE ATTENTION to the signs of your numbers when you add and subtract

2. COMBINE LIKE TERMS

1. DISTRIBUTE

SIMPLIFYING EXPRESSIONS

​MULTIPLYING INTEGERS SONG
Multiply or divide
It's an easy thought
Same signs are positive
Different signs are not

Math Response

Simplify the following expression by combining like terms:

$$4x-2x-20x+x$$

Type answer here

Correct Answer: -17x

Deg^°

Rad

Math Response

Simplify the following expression by combining like terms:

$$3.75x-5-8.75x+4.5+0.5$$

Type answer here

Correct Answer: -5x

Deg^°

Rad

Math Response

Simplify the following expression by combining like terms:

$$12\frac{5}{6}x-14x+\frac{1}{6}x$$

Type answer here

Correct Answer: -x

Deg^°

Rad

Math Response

Simplify the following expression by distributing:

$$-4\left(2x-3\right)$$

Type answer here

Correct Answer: -8x+12

Deg^°

Rad

Math Response

Simplify the following expression by distributing:

$$\frac{1}{2}\left(6x+10\right)$$

Type answer here

Correct Answer: 3x+5

Deg^°

Rad

Math Response

Simplify the following expression:

$$\frac{2}{3}\left(3x+12\right)+x$$

Type answer here

Correct Answer: 3x+8

Deg^°

Rad

Math Response

Simplify the following expression:

$$\frac{3}{4}x+2\left(9-\frac{1}{4}x\right)$$

Type answer here

Correct Answer: \frac{1}{4}x+18

Deg^°

Rad

One and Two Step Equations

Multiple Choice

What is your end goal when solving an equation?

• Isolate the variable

• Move all the numbers to a different side

• Get zero

• Do the math that is happening to the variable

Multiple Choice

What do you need to do to isolate the variable in the following equation?

$$\frac{x}{1.5}=60$$

• Divide both sides by 60

• Divide both sides by 1.5

• Multiply both sides by 60

• Multiply both sides by 1.5

Multiple Choice

What do you need to do to isolate the variable in the following equation?

$$-6+m=3.6$$

• Add 3.6 to both sides

• Add 6 to both sides

• Subtract 3.6 from both sides

• Subtract 6 from both sides

Multiple Choice

What do you need to do to isolate the variable in the following equation?

$$\frac{6}{7}e=12$$

• Subtract $$\frac{6}{7}$$ from both sides

• Multiply both sides by $$\frac{6}{7}$$

• Subtract $$\frac{7}{6}$$ from both sides

• Multiply both sides by $$\frac{7}{6}$$

Math Response

Solve the following equation to find what x equals:

$$\frac{x}{1.6}+31=40$$

Type in the number answer ( do not put x= )

Type answer here

Correct Answer: 14.4

Deg^°

Rad

Math Response

Solve the following equation to find what x equals:

$$-12=\frac{n}{2}-6$$

Type in the number answer ( do not put x= )

Type answer here

Correct Answer: -12

Deg^°

Rad

Math Response

Solve the following equation to find what x equals:

$$\frac{2}{3}x+19=35$$

Type in the number answer ( do not put x= )

Type answer here

Correct Answer: 24

Deg^°

Rad

Multi-Step Equations

There are 4 steps to solve equations

1. Distribute

2. Combine like terms

3. Add or subtract your constant
   (do the inverse of addition or subtraction)

4. Multiply or divide your coefficient
   (do the inverse of multiplication or division)

Multi-Step Equations

There are 4 steps to solve equations

1. Distribute

2. Combine like terms

3. Add or subtract your constant
   (do the inverse of addition or subtraction)

4. Multiply or divide your coefficient
   (do the inverse of multiplication or division)

​1-2) Steps to simplify

3-4) Steps to Isolate the variable and solve

​**Write down ALL your work from this slide. There will be questions from it after.

Fill in the Blanks

Solve the equation from the previous slide:

Type your NUMBER answer into the box below

Math Response

What was the cost of the SHOES?

Type answer here

Correct Answer: 32

Deg^°

Rad

Math Response

What was the cost of the SHIRT?

Type answer here

Correct Answer: 16

Deg^°

Rad

Math Response

What was the cost of the SUNGLASSES?

Type answer here

Correct Answer: 8

Deg^°

Rad

Math Response

Solve the equation from the previous slide.

Type your answer into the box

Type answer here

Correct Answer: 2.50

Deg^°

Rad

Multiple Select

Which option is equivalent to:
$$\frac{1}{2}b$$

Choose ALL that are correct

• $$2b$$

• $$\frac{b}{2}$$

• $$2\div b$$

• $$b\div2$$

Math Response

Solve the equation below:

$$18-5w+7w-4=28$$

Type answer here

Correct Answer: 7

Deg^°

Rad

Math Response

Solve the equation below:

$$4x-4\left(7-5x\right)=-20$$

Type answer here

Correct Answer: \frac{1}{3}

Deg^°

Rad

Math Response

Solve the equation below:

$$\frac{2}{3}\left(6x+30\right)+8=80$$

Type answer here

Correct Answer: 13

Deg^°

Rad

Math Response

Solve the equation below:

$$44=17n-23n+11.5n$$

Type answer here

Correct Answer: 8

Deg^°

Rad