Exercise 9 Page 277

Practice makes perfect

To solve the given equation for y, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.

4x-2+y=6-2x

SubEqn

LHS-4x=RHS-4x

- 2+y=6-6x

AddEqn

LHS+2=RHS+2

y=8-6x

We are asked to solve the given equation for x. 4x-2+y=6-2xTo do this, we will first isolate the x-term on the left-hand side of the equation using the Addition and Subtraction Properties of Equality.

4x-2+y=6-2x

AddEqn

LHS+2x=RHS+2x

6x-2+y=6

SubEqn

LHS-y=RHS-y

6x-2=- y +6

AddEqn

LHS+2=RHS+2

6x=- y +8

Next, we will use the Division Property of Equality to solve for x.

6x=- y +8

DivEqn

.LHS /6.=.RHS /6.

6x/6=- y +8/6

WriteDiffFrac

Write as a difference of fractions

6x/6=- y/6+8/6

MovePartNumRight

a* b/c=a/c* b

6x/6=- 1/6y+8/6

SimpQuot

Simplify quotient

x=- 1/6y+8/6

MoveNegNumToFrac

Put minus sign in front of fraction

x=-1/6y+8/6

We will solve the following equation for x. 3(6-x)+2x=15 To do this, we will use the properties of equality to apply inverse operations on the equation. Remember, only like terms can be combined.

3(6-x)+2x=15

Distr

Distribute 3

3(6)-3(x)+2x=15

Multiply

18-3x+2x=15

AddTerms

Add terms

18-x=15

SubEqn

LHS-18=RHS-18

- x=- 3