Expressions and Equations

A short lesson on
1) Simplifying
2) Solving

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​Linear Expressions and Equations

Combine Like Terms

Like terms are combined by adding/subtracting the coefficients

Match

Match the following

• variable

• coefficient

• constant

a letter representing an unknown number

a number multiplying a variable

a number without a variable

• a letter representing an unknown number

• a number multiplying a variable

• a number without a variable

Multiple Choice

Translate:
Five more than a number

• x + 5

• 5x

• 5 - x

• 5 divided by x

Multiple Choice

Translate: 
Four times a number plus six is thirty.

• 4 + 6 = 30

• 4x + 6 = 30

• x + 4 times 6 = 30

• 30 = 4x

Expressions vs. Equations

• Expressions: numbers, letters, and operators grouped together to represent a value

• NO = SIGN , CANNOT ALWAYS SOLVE!

• Equations: states that two expressions are equal

• HAS = SIGN, CAN SOLVE FOR THE VARIABLE!

Multiple Choice

Which of the following is an equation?

• $$-17+9$$
  

• $$-17+9=-8$$
  

Multiple Choice

Pick out the expression.

• 
  

  $$5x+4-9=22$$  

• $$25=-5x$$
  

• $$4a-3c+15-12a$$  

• $$6\left(x-3\right)=52$$  

Multiple Choice

Which of the following is not an equation?

• 2x+5=12

• 5+12

• 5m-8=24

• -8=x-9

Multiple Choice

$$4m-7+8m-17$$  True or False: I can solve an algebraic expression like the one below and get an answer like x=#.

• True

• False

FALSE

Algebraic expressions cannot be solved! You can only simplify them (combine like terms or use distributive property). You should never get an answer of x=# with algrebaic expressions.

One-Step Equations

• GOAL: GET VARIABLE BY ITSELF!

• To do this: get rid of the number on the same side of the equation as the varibale by using inverse operations!

Fill in the Blanks

$x-19=12$  

Fill in the Blanks

$\frac{a}{12}=-4$  

Fill in the Blanks

$13=9+m$  

Fill in the Blanks

$8y=52$  

Fill in the Blanks

$-7g=-84$  

Fill in the Blanks

$b-\left(-14\right)=9$  

Fill in the Blanks

$-\frac{n}{8}=13$  

Fill in the Blanks

$-x=-54$  

Multiple Choice

a mathematical sentence stating that two expressions are equal. Always has an equal sign.

• term

• coefficient

• equation

• variable

Multiple Choice

What is the inverse operation of subtraction?

• Subtraction

• Multiplication

• Division

• Addition

Multiple Choice

What is the inverse operation of division?

• Division

• Multiplication

• Addition

• Subtraction

Multiple Choice

When solving 234 + N =389, what operation would you use to find the answer

• multiplication

• addition

• subtraction

• division

Multiple Choice

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

• Add 62 to each side. 

• Subtract 62 from each side.

• Multiply each side by 62.

• Add 123 to each side.

Multiple Choice

What equation matches this situation?
Robyn had some video games then bought 4 more.  Now she has a total of 10 games.

• v - 4 = 10

• v + 4 = 10

• 10 - 4 = v

• Answer not Given