Exercise 61 Page 414

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

2(x+4.5)=32

Distr

Distribute 2

2(x)+2(4.5)=32

Multiply

2x+9=32

Now we can continue to solve using the properties of equality.

2x+9=32

SubEqn

LHS-9=RHS-9

2x=23

DivEqn

.LHS /2.=.RHS /2.

2x/2=23/2

SimpQuot

Simplify quotient

x=23/2

CalcQuot

Calculate quotient

x=11.5

The solution to the equation is x=11.5. We can check our solution by substituting it into the original equation. If simplifying results in a true statement, we know our answer is correct. Let's do it!

2(x+4.5)=32

Substitute

x= 11.5

2( 11.5+4.5) ? = 32

▼

Simplify

AddTerms

Add terms

2(16) ? = 32

Multiply

32 = 32 ✓

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

We are asked to solve the given equation. To do so, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality.

6+2.5x=21

SubEqn

LHS-6=RHS-6

2.5x=15

DivEqn

.LHS /2.5.=.RHS /2.5.

2.5x/2.5=15/2.5

SimpQuot

Simplify quotient

x=15/2.5

CalcQuot

Calculate quotient

x=6

The solution to the equation is x=6. Let's check our solution by substituting it into the original equation.

6+2.5x=21

Substitute

x= 6

6+2.5( 6) ? = 21

▼

Simplify

Multiply

6+15 ? = 21

AddTerms

Add terms

21 = 21 ✓

Our solution is correct because the left-hand side is equal to the right-hand side.

We want to solve the given equation. We can start by gathering all of the variable terms on one side and all of the constant terms on the other side using cross products and the properties of equality.

x/9=5/16

CrossMult

Cross multiply

x(16)=9(5)

Multiply

16x=45

DivEqn

.LHS /16.=.RHS /16.

16x/16=45/16

SimpQuot

Simplify quotient

x=45/16