Exercise 3 Page 247

To graph the equation - 2x+3=x, we will create two functions out of the left- and right-hand sides of the equation. f(x)=- 2x+3 and g(x)=x The x-coordinate where the graphs of these functions intersect is the solution to our equation.

The graphs intersect at x=1, which is our solution. We can verify this algebraically by solving the equation.

- 2x+3=x

AddEqn

LHS+2x=RHS+2x

3=3x

DivEqn

.LHS /3.=.RHS /3.

1=x

RearrangeEqn

Rearrange equation

x=1

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.

- 2x+3=x

Substitute

x= 1

- 2( 1)+3? = 1

IdPropMult

Identity Property of Multiplication

- 2+3? =1

AddTerms

Add terms

1=1 ✓