Exercise 6 Page 265

To graph the equation - 32x-2=- 4x+3, we will create two functions out of the left- and right-hand sides of the equation. f(x)=-3/2 x-2 and g(x)=- 4x+3 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.

-3/2x-2=- 4x+3

MultEqn

LHS * 2=RHS* 2

- 3x-4=- 8x+6

AddEqn

LHS+8x=RHS+8x

5x-4=6

AddEqn

LHS+4=RHS+4

5x=10

DivEqn

.LHS /5.=.RHS /5.

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.

-3/2x-2=- 4x+3

Substitute

x= 2

-3/2( 2)-2? =- 4( 2)+3

MultNegPos

(- a)b = - ab

- 3-2? =- 8+3

AddSubTerms

Add and subtract terms

- 5=- 5 ✓