EquationsEquations

Live Chat #3Live Chat #3

Instructor: Tonya Andry-Instructor: Tonya Andry-StelterStelter

What Does it Mean to Solve an What Does it Mean to Solve an Equation?Equation?

To solve an equation means to find every number that makes the equation true.

We do this by adding or subtracting to each side of the equation … but always keep it balanced!

What are the parts of an equation?What are the parts of an equation?

Let’s first take a look at an Let’s first take a look at an equation and identify its partsequation and identify its parts

3 1 2 3 6x x

Coefficient

ConstantVariable

So do we just use trial and error to So do we just use trial and error to find the right value?find the right value?

No. No. We can use We can use inverse operationsinverse operations to to

isolate, or solve for, the variable’s isolate, or solve for, the variable’s value.value.

Inverse operations? Think about it …Inverse operations? Think about it …The inverse operation of addition is The inverse operation of addition is subtractionsubtraction. And the inverse . And the inverse operation of multiplication is operation of multiplication is divisiondivision..

Solving 1 Step EquationsSolving 1 Step Equations

How much does the suitcase weigh

in terms of blocks?

B=Blocks S=Suitcase

Equation: 6B + S = 9B

-6B

-6B

3BS =What is the weight of the suitcase if each

block has a weight of 2lbs. ?

S = 3 (2) = 6 lbs.

So how do we solve equations with So how do we solve equations with inverse operations?inverse operations?

Let’s take a look at a simple equationLet’s take a look at a simple equation

Step 1:- 13

Answer:

2113 x- 13

8x

Now that we have solved the equation, let’s check the solution:

2121

2113 x21138

So how do we solve equations with So how do we solve equations with inverse operations?inverse operations?

Let’s take a look at a simple equationLet’s take a look at a simple equation

Step 1:+ 5

Answer:

125 y+ 5

17y

Now that we have solved the equation, let’s check the solution:

1212

125 y

12517

So how do we solve equations with So how do we solve equations with inverse operations?inverse operations?

Let’s take a look at a simple equationLet’s take a look at a simple equation

Step 1:

Step 2:

25

Answer:

7525 W25

25

75W

3W

Now that we have solved the equation, let’s check the solution:

7525 W

75)3(25

7575

So how do we solve equations with So how do we solve equations with inverse operations?inverse operations?

Let’s take a look at a simple equationLet’s take a look at a simple equation

Step 1:

Step 2:

(16)

Answer:

416

A

(16)

)16(4A

64A

Now that we have solved the equation, let’s check the solution:

44

416

A

416

64

1 Step Equation1 Step Equation

X + 11 = 9 X - 37 = 52 3X = 72-11 -

11X = -2

3 3

X = 24

1

1

20 + h = 41 17 - s = 27

1 Step Equations Continued…1 Step Equations Continued…X / 5 = 10X / 7 = 46X = 42

25

P = 34

3 / s = 21

Multi Step Equations

Solve:

8m – 10 = 36

423

31176w

8m – 10 = 36

8m = 468 8

m =

+ 10 + 10

Multi Step EquationsMulti Step Equations

5x 2 = x + 4 Solve:

5x 2 = x + 4

Notice that there are variables on both sides

5x = x + 6

Get rid of the -2 on the left side

Simplify

5x = x + 6Get rid of the x on the right side4x = 6Get rid of the coefficient of x

4 4

23x = Simplify

Simplify

+ 2 + 2

– x– x

Solving a ProportionSolving a Proportion

Solve the proportion belowSolve the proportion below

60

126

C)12()60(6 C

C12360 12 12

C30

Solving a ProportionSolving a Proportion

Solve the proportion belowSolve the proportion below

852

13 a )(52)8(13 a

a52104 52 52

a2

Checking the Solution to a Checking the Solution to a ProportionProportion

Let’s check the solution to the Let’s check the solution to the proportion we solved on the last slideproportion we solved on the last slide

852

13 a

852

13

2

4

1

4

1

Using Proportions to Solve Using Proportions to Solve ProblemsProblems

You get 46 miles to a gallon of gas. You get 46 miles to a gallon of gas. How far can you go on 16 gallons of How far can you go on 16 gallons of gas?gas?

m

16

46

1 )16(461 m

736m

Word ProblemsWord Problems

A company purchased 5,000 pairs of men’s A company purchased 5,000 pairs of men’s slacks for $15.86 per pair and marked them slacks for $15.86 per pair and marked them up $24.54. What was the selling price for up $24.54. What was the selling price for each pair of slacks? Use the formula each pair of slacks? Use the formula S=C+M. S=selling price, C=Original Cost, S=C+M. S=selling price, C=Original Cost, M=Mark up.M=Mark up.

Fishing Pole PriceFishing Pole PriceTracee and her husband bought a fishing pole for Tracee and her husband bought a fishing pole for

$62.45 for their weekend camping trip. The store $62.45 for their weekend camping trip. The store they bought the poles from had marked them up they bought the poles from had marked them up $27.35. What was the original cost of the fishing $27.35. What was the original cost of the fishing poles for the store? Use the formula S = C + Mpoles for the store? Use the formula S = C + M

Two part time employees share one full-time Two part time employees share one full-time position. Rosalind works Mondays, position. Rosalind works Mondays, Wednesdays, Fridays and Saturdays. Wednesdays, Fridays and Saturdays. Sherman works Tuesdays and Thursdays. The Sherman works Tuesdays and Thursdays. The job pays an annual salary of $45, 679. What job pays an annual salary of $45, 679. What annual salary does each employee earn?annual salary does each employee earn?

Annual Earnings

Money ConversionMoney Conversion

Tyesha is moving to Germany in the summer. Tyesha is moving to Germany in the summer. She will need to convert some of her money She will need to convert some of her money before she leaves. If 1.00 US Dollar is equal to before she leaves. If 1.00 US Dollar is equal to 0.734916 Euros then how much money should 0.734916 Euros then how much money should she expect to get if she converts $650?she expect to get if she converts $650?

Material CostMaterial CostVeronica is an inspector who also buys material Veronica is an inspector who also buys material for the job site. She needs to buy 3 times as for the job site. She needs to buy 3 times as many yards of soil as yards of concrete. If a yard many yards of soil as yards of concrete. If a yard of concrete costs about $70 and a yard of soil of concrete costs about $70 and a yard of soil costs about $57 and her total order was roughly costs about $57 and her total order was roughly $8378 how many yards of each did she order? $8378 how many yards of each did she order?

$8378 = $70C + $57S

Total Cost = Concrete Cost + Soil Cost

3 times as much soil as concreteS = 3C

$8378 = $70C + $57(3C)

$8378 = $70C + $171C

$8378 = $241C

$8378$241

= C

C ≈ 34.76 yds

S = 3(34.76)S = 104.28yds.

Using Proportions to Solve Problems

Your trimmer uses fuel that is a 1:50 ratio of oil to gas. If you have 68oz of gas, how much oil should you add?

gasoz

oiloz

50

1

gasoz

x

68

x5068 x36.1

Recipes (Proportions)Recipes (Proportions)Dawn enjoys cooking and wants to make a tasty Dawn enjoys cooking and wants to make a tasty

dessert for her family. Her recipe uses 3 cups of dessert for her family. Her recipe uses 3 cups of sugar to 2 ¼ cups of flour. But she only has 2 sugar to 2 ¼ cups of flour. But she only has 2 cups of sugar, how much flour should you use?cups of sugar, how much flour should you use?

3

2 ¼2 ¼=

2

XX

Recipe SugarRecipe FlourRecipe Flour

=New Amount of Sugar

New Amount of New Amount of FlourFlour

3 ● X

=

= 2 ● 9/43X = 4.5

X = 1.5