Exercise 40 Page 25

Practice makes perfect

a To solve the given equation, we should start by multiplying both sides of the equation by 3 in order to remove the fractions.

x/3= 6

MultEqn

LHS * 3=RHS* 3

x/3(3)= 6(3)

FracMultDenomToNumber

a/3* 3 = a

x=6(3)

Multiply

x=18

The solution to the equation is x=18. We can check our solution by substituting it into the original equation.

x/3= 6

Substitute

x= 18

18/3 ? = 6

CalcQuot

Calculate quotient

6=6 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

b To solve the given equation, we should start by multiplying both sides of the equation by 2 in order to remove fractions. Then we will gather all of the variable terms on one side of the equation and all constants on the other side by using the Properties of Equality.

5x+9/2= 12

MultEqn

LHS * 2=RHS* 2

5x+9/2(2)= 12(2)

FracMultDenomToNumber

a/2* 2 = a

5x+9= 24

SubEqn

LHS-9=RHS-9

5x=15

DivEqn

.LHS /5.=.RHS /5.

x= 3

The solution to the equation is x=3. We can check our solution by substituting it into the original equation.

5x+9/2= 12

Substitute

x= 3

5( 3)+9/2 ? = 12

▼

Simplify

Multiply

15+9/2 ? = 12

AddTerms

Add terms

24/2 ? = 12

CalcQuot

Calculate quotient

12=12 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

c To solve the given equation, we will start by multiplying both sides of the equation by the lowest common denominator to remove fractions. Then we will isolate the variable on the one side of the equation by using the Properties of Equality.

x/4=9/6

MultEqn

LHS * 12=RHS* 12

x/4(12)=9/6(12)

SplitIntoFactors

Split into factors

x/4(4)(3)=9/6(6)(2)

FracMultDenomToNumber

a/4* 4 = a

x(3)=9/6(6)(2)

FracMultDenomToNumber

a/6* 6 = a

x(3)=9(2)

Multiply

3x=18

DivEqn

.LHS /3.=.RHS /3.

x=6

The solution to the equation is x=6. We can check our solution by substituting it into the original equation.

x/4=9/6

Substitute

x= 6

6/4 ? = 9/3

▼

Simplify

ReduceFrac

a/b=.a /2./.b /2.

3/2 ? = 9/3

ReduceFrac

a/b=.a /3./.b /3.

3/2=3/2 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.

d To solve the given equation, we will start by multiplying both sides of the equation by the lowest common denominator to remove fractions. Then we will isolate the variable on the one side of the equation by using the Properties of Equality.

5/x=20/8

MultEqn

LHS * 8x=RHS* 8x

5/x(8x)=20/8(8x)

SplitIntoFactors

Split into factors

5/x(x)(8)=20/8(8)(x)

FracMultDenomToNumber

a/x* x = a

5(8)=20/8(8)(x)

FracMultDenomToNumber

a/8* 8 = a