Exercise 6 Page 190

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. Let's do it!

2x+22=12

SubEqn

LHS-22=RHS-22

2x+22-22=12-22

SubTerms

Subtract terms

2x=- 10

DivEqn

.LHS /2.=.RHS /2.

2x/2=- 10/2

CalcQuot

Calculate quotient

x= - 5

The solution to the equation is x=- 5.

To solve an equation for y, we should first gather all of the y-terms on one side and all of the other terms on the other side using the properties of equality. Let's do it!

2x-y=3

AddEqn

LHS+y=RHS+y

2x-y+y=3+y

AddTerms

Add terms

2x=3+y

SubEqn

LHS-3=RHS-3

2x-3=3+y-3

SubTerms

Subtract terms

2x-3=y

RearrangeEqn

Rearrange equation

y=2x-3

The solution to the equation is y=2x-3.

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. Let's do it!

2x+15=2x-15

SubEqn

LHS-15=RHS-15

2x+15-15=2x-15-15

SubTerms

Subtract terms

2x=2x-30

SubEqn

LHS-2x=RHS-2x

2x-2x=2x-30-2x

SubTerms

Subtract terms

0≠ - 30 *

Notice that solving the equation for x resulted in a false statement. This means that the given equation has no solution.

To solve an equation for y, we should first gather all of the y-terms on one side and all of the other terms on the other side using the properties of equality. Let's do it!

6x+2y=10

SubEqn

LHS-6x=RHS-6x

6x+2y-6x=10-6x

SubTerms

Subtract terms

2y=10-6x

DivEqn

.LHS /2.=.RHS /2.

2y/2=10-6x/2

SimpQuot

Simplify quotient