Exercise 5 Page 247

To graph the equation - x-1= 13x+3, we will create two functions out of the left- and right-hand sides of the equation. f(x)=- x-1 and g(x)=1/3x+3 The x-coordinate where the graphs of these functions intersect is the solution to our equation.

The graphs intersect at x=- 3, which is our solution. We can verify this algebraically by solving the equation.

- x-1=1/3x+3

MultEqn

LHS * 3=RHS* 3

3(- x-1)=3(1/3x+3)

▼

Simplify

Distr

Distribute 3

3(- x)-3(1)=3(1/3x)+3(3)

DenomMultFracToNumber

3 * a/3= a

3(- x)-3(1)=(1)x+3(3)

IdPropMult

Identity Property of Multiplication

3(- x)-3=x+3(3)

MultPosNeg

a(- b)=- a * b

- 3x-3=x+3(3)

Multiply

Multiply

- 3x-3=x+9

SubEqn

LHS-x=RHS-x

- 4x-3=9

AddEqn

LHS+3=RHS+3

- 4x=12

DivEqn

.LHS /(- 4).=.RHS /(- 4).

x=12/- 4

MoveNegDenomToFrac

Put minus sign in front of fraction

x=- 12/4

CalcQuot

Calculate quotient

x=- 3

To check this solution, we will substitute it back into the given equation and simplify. If doing so results in a true statement, our solution is correct.

- x-1=1/3x+3

Substitute

x= - 3

- ( - 3)-1? =1/3( - 3)+3

NegNeg

- (- a)=a

3-1? =1/3(- 3)+3

MultPosNeg

a(- b)=- a * b

3-1? =- 1+3

AddSubTerms

Add and subtract terms

2=2 ✓