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Core Connections Algebra 1, 2013
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Core Connections Algebra 1, 2013 View details
2. Section 1.2
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Exercise 67 Page 30

Practice makes perfect
a To solve the equation for x, we have to isolate it on one side of the equation by performing inverse operations.
6-x-3=10
SubTerm

Subtract term

3-x=10
SubEqn

LHS-3=RHS-3

- x=7
MultEqn

LHS * (- 1)=RHS* (- 1)

x=- 7
We will check the solution by substituting it into the equation.
6-x-3=10
Substitute

x= - 7

6-( - 7)-3? =10
SubNeg

a-(- b)=a+b

6+7-3? =10
AddSubTerms

Add and subtract terms

10=10
The solution is correct.
b Again, let's perform inverse operations until x is isolated.
100x+300=200
SubEqn

LHS-300=RHS-300

100x=- 100
DivEqn

.LHS /100.=.RHS /100.

x=- 1
We will check the solution by substituting it into the equation.
100x+300=200
Substitute

x= - 1

100( - 1)+300 ? =200
MultPosNeg

a(- b)=- a * b

- 100+300 ? =200
AddTerms

Add terms

200=200
The solution is correct.
c Again, we will isolate x by performing inverse operations.
1/3x+4=x-2
AddEqn

LHS+2=RHS+2

1/3x+6=x
MultEqn

LHS * 3=RHS* 3

x+18=3x
SubEqn

LHS-x=RHS-x

18=2x
DivEqn

.LHS /2.=.RHS /2.

9=x
RearrangeEqn

Rearrange equation

x=9
Let's check the solution by substituting it into the equation.
1/3x+4=x-2
Substitute

x= 9

1/3* 9+4 ? = 9-2
MoveRightFacToNumOne

1/b* a = a/b

9/3+4 ? =9-2
CalcQuot

Calculate quotient

3+4 ? =9-2
AddSubTerms

Add and subtract terms

7=7
The solution is correct.
d Again, we will isolate x.
36-2x=- x+2
SubEqn

LHS-2=RHS-2

34-2x=- x
AddEqn

LHS+2x=RHS+2x

34=x
RearrangeEqn

Rearrange equation

x=34
Let's now check this solution by substituting it into the equation. If it makes a true statement, then our solution is correct.
36-2x=- x+2
Substitute

x= 34

36-2( 34)? =- 34+2
Multiply

Multiply

36-68? =- 34+2
AddSubTerms

Add and subtract terms

- 32=- 32
As we can see, x=34 is a correct solution.
Subchapter links expand_more
arrow_right 1.2.1 Describing a Graph p.19-21
33
Describing a Graph 34 (Page 19)
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Describing a Graph 36 (Page 20)
Describing a Graph 37 (Page 20)
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Describing a Graph 39 (Page 20)
Describing a Graph 40 (Page 21)
Describing a Graph 41 (Page 21)
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arrow_right 1.2.2 Cube Root and Absolute Value Functions p.23-24
47
Cube Root and Absolute Value Functions 48 (Page 23)
Cube Root and Absolute Value Functions 49 (Page 24)
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Cube Root and Absolute Value Functions 51 (Page 24)
arrow_right 1.2.3 Function Machines p.27
57
Function Machines 58 (Page 27)
Function Machines 59 (Page 27)
60
Function Machines 61 (Page 27)
arrow_right 1.2.4 Functions p.30-31
Functions 66 (Page 30)
Functions 67 (Page 30)
Functions 68 (Page 30)
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70
arrow_right 1.2.5 Domain and Range p.36
Domain and Range 78 (Page 36)
Domain and Range 79 (Page 36)
80
81
Domain and Range 82 (Page 36)