Chapter Closure
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Exercise 121 Page 430
We want to solve the given equation.
5x+2=- 3x-14
We can start by using the Addition Property of Equality to isolate the variables on the left-hand side of the equation and constants on the right-hand side of the equation.
5x+2=- 3x-14
AddEqn
LHS+3x=RHS+3x
5x+2+3x=- 3x-14+3x
CommutativePropAdd
Commutative Property of Addition
5x+3x+2=- 3x+3x-14
AddTerms
Add terms
8x+2=- 14
SubEqn
LHS-2=RHS-2
8x+2-2=- 14-2
SubTerm
Subtract term
8x=- 16
Next, we can use the Division Property of Equality to simplify the equation even further.
8x=- 16
DivEqn
.LHS /8.=.RHS /8.
8x/8=- 16/8
MovePartNumRight
a* b/c=a/c* b
8/8x=- 16/8
QuotOne
a/a=1
1x=- 16/8
IdPropMult
Identity Property of Multiplication
x=- 16/8
MoveNegNumToFrac
Put minus sign in front of fraction
x=-16/8
CalcQuot
Calculate quotient
x=- 2
We want to solve the given equation.
23x+1=x-4
We can start by using the Subtraction Property of Equality to isolate the variables on the left-hand side of the equation and constants on the right-hand side of the equation.
23x+1=x-4
SubEqn
LHS- 23x=RHS- 23x
23x+1- 23x=x-4- 23x
CommutativePropAdd
Commutative Property of Addition
23x- 23x+1=x- 23x-4
SubTerm
Subtract term
1=x- 23x-4
AddEqn
LHS+4=RHS+4
1+4=x- 23x-4+4
AddTerms
Add terms
5=x- 23x
FactorOut
Factor out x
5=x(1-2/3)
NumberToFrac
a = 3* a/3
5=x(3/3-2/3)
SubFrac
Subtract fractions
5=x(1/3)
Next, we can use the Multiplication Property of Equality to simplify the equation even further.
5=x(1/3)
MultEqn
LHS * 3=RHS* 3
5* 3=x(1/3)* 3
Multiply
Multiply
15=x(1/3)* 3
NumberToDenomMultFrac
a = 3 * a/3
15=x(1)
IdPropMult
Identity Property of Multiplication
15=x
RearrangeEqn
Rearrange equation
x=15
We want to solve the given equation.
0.5x-0.5=0.75x+1-x
We can start by simplifying the right-hand side of the equation using the Commutative Property of Addition.
0.5x-0.5=0.75x+1-x
▼
Subtract term
- 0.5+0.5x=1-0.25x
AddEqn
LHS+0.25x=RHS+0.25x
- 0.5+0.5x+0.25x=1-0.25x+0.25x
AddTerms
Add terms
- 0.5+0.75x=1
AddEqn
LHS+0.5=RHS+0.5
- 0.5+0.75x+0.5=1+0.5
▼
Add terms
0.75x=1.5
Next, we can use the Division Property of Equality to simplify the equation even further.
0.75x=1.5
DivEqn
.LHS /0.75.=.RHS /0.75.
0.75x/0.75=1.5/0.75
MovePartNumRight
a* b/c=a/c* b
0.75/0.75x=1.5/0.75
QuotOne
a/a=1
1x=1.5/0.75
IdPropMult
Identity Property of Multiplication
x=1.5/0.75
CalcQuot
Calculate quotient
x=2
We want to solve the given equation.
5x+6-2x=3x-7
We can start by simplifying the left-hand side of the equation using the Commutative Property of Addition.
5x+6-2x=3x-7
SubEqn
LHS-3x=RHS-3x
5x+6-2x-3x=3x-7-3x
CommutativePropAdd
Commutative Property of Addition
5x-2x-3x+6=3x-3x-7
SubTerm
Subtract term
6 ≠ - 7
In this case, our equation has no solutions.
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