Expressions and Equations Review

Expressions and Equations Review

Order of operations(4.1)

• Remember the order of operations for use to be ale to simplify equations

• P(arentheses) E(xponents) M(ultiplication) D(ivision) A(ddition) S(ubtraction)

• remember that Multiplication, and Division can be switched. It is whichever comes first from reading the expression from left to right.

• same thing as above with addition and subtraction,

Multiple Choice

SImplifying using order of operations

• 1

• 2

• 3

• 4

Multiple Choice

Simplify. (7-4)² + (20-19) - 10

• -3

• 57

• 0

• 1

Evaluating expressions 

• When evaluating expressions, remember to plug in/replace your given variables first, then simplify.

•  $4x+5^2$  when x=2 turns into 

•  $4\cdot2+5^2$  then we follow our Order of Operations to simplify

•  $4\cdot2+\left(5\cdot5\right)=4\cdot2+25$  

•  $8+25=33$  

Multiple Choice

Simplify 8y + 12 - 2z

for y = 4 and z = 2

• 40

• 20

• 84

• 34

Multiple Choice

Simplify b² + 4

when b = 3

• 10

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Combining Like Terms

• Remember like terms are parts of an expression that have the exact same variable parts.

• for example: 2x and 3x are like terms because they both have x.

•  $2x^2$  and 3x, they would not be like terms because their variables are not the exact same.  $x^{2\ }$  is different than x

  
  

• If they are like terms, then we can combine them by adding or subtracting them to their like terms. 

Examples

• Let us combine like terms in the expression

   $3m+6+5m=$  
  

•  $3m+5m+6=$  we can move the 5m to be next to the three as long as we add the 5m

•  $8m+6$  then we can add 3m and 5m to get 8m and we have to bring down our other terms with it. 

Multiple Choice

Simplify: 2x+3+9x+2

• 16x

• 11x+5

• 5x+11

• 16+x

Multiple Choice

Combine like terms

• 7x²+3x+5

• 9x²+4x+5

• 4x +9x²+5

• 9x²+3x+5

Solving equations

• When we solve equations, we have to do the opposite or inverse operation to help us solve.

• Our main goal is to isolate our variable or that our variable is by itself on one side of an equation so that we can find the missing value.

• that looks like " x=9"

Solving Equations Continued

• so for addition equations or x+9=12; you will subtract the number that is being added to x from both sides so that our x is by itself.

• You would then have x=12-9 and then you can subtract from there.

• You should get an answer of x=3.

It works the same for other equations

• for subtraction equations (x-2=7) you would add two to both sides

• for multiplication equations (4x=8) you would divide 4 by both sides

• for division equations ( $\frac{x}{5}=3$  ) you would multiply 5 by both sides 

  
  

• remember that when you answer you have the variable on one side(x=_), that is telling me that that variable has a value and we found the value. 

Multiple Choice

Which equation has x = 5 as the solution?

• x + 15 = 10

• 2x = 5

• 2x = 10

Multiple Choice

y - 4.6 = 12

• 16.6

• 5.8

• 7.4

• Answer not Given

Multiple Choice

y - 4.6 = 12

• 16.6

• 5.8

• 7.4

• Answer not Given

Using Formulas

• Now that we have had practice with solving for missing variables we can use formulas with given numbers, to help us find more missing values.

• With formulas, you will always be given the formula needed and the values needed.

Example

• We are going to use the formula for Volume which is

   $V=l\cdot w\cdot h$   where V=2304, l=32, w=_, and h=8

• first, substitute the values we know. so  $2304=32\cdot w\cdot8$  

• Then, you can multiply 32 and 8 to get  $2304=256\cdot w$  

• After, you can solve for w by dividing both sides by 256 to get w=9

Multiple Choice

Use the formula P=5s where P=240 and s=_. Find the missing value for s.

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Multiple Choice

Use the formula

 $A=\frac{1}{2}bh$  when A=200 and h=10 and b=_. Find the missing value for b. 

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Multiple Choice

Use the formula

 $P=2\left(l+w\right)\$  when l=7 and w=4 and P=_. Find the missing value for P.

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• 41