Exercise 96 Page 149

Practice makes perfect

a To solve the proportion, we will start by using cross products. Remember that we will need to treat m+1 as a single quantity in the cross multiplication process.

m/6=m+1/5

CrossMult

Cross multiply

m(5)=6(m+1)

Multiply

5m=6(m+1)

From here, we will continue solving for m by using the Distributive Property and the Properties of Equality.

5m=6(m+1)

Distr

Distribute 6

5m=6m+6

SubEqn

LHS-6m=RHS-6m

- m=6

MultEqn

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

m=-6

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

m/6=m+1/5

Substitute

m= -6

-6/6 ? = -6+1/5

▼

Simplify

AddTerms

Add terms

-6/6 ? = -5/5

MoveNegNumToFrac

Put minus sign in front of fraction

-6/6 ? = -5/5

CalcQuot

Calculate quotient

-1=-1

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

b To solve the proportion, we will start by using cross products. Remember that we will need to treat 3x-5 and 4x+1 as single quantities in the cross multiplication process.

3x-5/2=4x+1/4

CrossMult

Cross multiply

(3x-5)4=2(4x+1)

CommutativePropMult

Commutative Property of Multiplication

4(3x-5)=2(4x+1)

From here, we will continue solving for x by using the Distributive Property and the Properties of Equality.

4(3x-5)=2(4x+1)

Distr

Distribute 4

12x-20=2(4x+1)

Distr

Distribute 2

12x-20=8x+2

▼

Simplify

SubEqn

LHS-8x=RHS-8x

4x-20=2

AddEqn

LHS+20=RHS+20

4x=22

DivEqn

.LHS /4.=.RHS /4.

x=22/4

ReduceFrac

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

x=11/2

The solution to the equation is x= 112. We can check our solution by substituting it into the original equation.

3x-5/2=4x+1/4

Substitute

x= 11/2

3( 112)-5/2 ? = 4( 112)+1/4

▼

Simplify

MoveLeftFacToNum

a*b/c= a* b/c

332-5/2? = 442+1/4

CalcQuot

Calculate quotient

332-5/2? = 22+1/4

AddTerms

Add terms

332-5/2? = 23/4

NumberToFrac

a = 2* a/2

332- 102/2? = 23/4

SubFrac

Subtract fractions

232/2? = 23/4

DivFracSL

.a/b /c.= a/b* c

23/4=23/4

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

c To solve the proportion, we will start by using cross products. Remember that we will need to treat k+3 as a single quantity in the cross multiplication process.

8/k=14/k+3

CrossMult

Cross multiply

8(k+3)=14(k)

Multiply

8(k+3)=14k

From here, we will continue solving for k by using the Distributive Property and the Properties of Equality.

8(k+3)=14k

Distr

Distribute 8

8k+24=14k

SubEqn