Exercise 2 Page 244

To graph the equation - 4+9x=- 3x+2, we create two functions out of the left- and right-hand sides of the equation. f(x)=- 4+9x and g(x)=- 3x+2 The x-coordinate where the graphs of these functions intersect is the solution to our equation. Since the given equations are not in slope-intercept form, let's rewrite them so that it will be easier to identify their slopes and y-intercepts.

y=- 4+9x

CommutativePropAdd

Commutative Property of Addition

y=9x-4

Now, let's graph these lines.

The graphs intersect at x=0.5, which is our solution. We can verify this algebraically by solving the equation.

- 4+9x=- 3x+2

AddEqn

LHS+4=RHS+4

9x=- 3x+6

AddEqn

LHS+3x=RHS+3x

12x=6

DivEqn

.LHS /12.=.RHS /12.

x=6/12

CalcQuot

Calculate quotient

x=0.5

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.

-4+9x=- 3x+2

Substitute

x= 0.5

-4+9( 0.5)? =- 3( 0.5)+2

Multiply

Multiply

-4+4.5? =- 1.5+2

AddTerms

Add terms

0.5=0.5 ✓