Exercise 1 Page 244

To graph the equation 12x-3=2x, we create two functions out of the left- and right-hand sides of the equation. f(x)=1/2x-3 and g(x)=2x The x-coordinate where the graphs of these functions intersect is the solution to our equation.

The graphs intersect at x=- 2, which is our solution. We can verify this algebraically by solving the equation.

1/2x-3=2x

SubEqn

LHS-1/2x=RHS-1/2x

- 3=3/2x

MultEqn

LHS * 2/3=RHS* 2/3

- 2=x

RearrangeEqn

Rearrange equation

x=- 2

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.

1/2x-3=2x

Substitute

x= - 2

1/2( - 2)-3? =2( - 2)

MultPosNeg

a(- b)=- a * b

- 1-3? =- 4

SubTerm

Subtract term

- 4=- 4