Exercise 11 Page 265

To graph the equation 12x-2=9-5x, we will create two functions out of the left- and right-hand sides of the equation. f(x)=1/2x-2 and g(x)=9-5x The x-coordinate where the graphs of these functions intersect is the solution to our equation. Since one of the given equations is not in slope-intercept form, let's rewrite it so that it will be easier to identify its slope and y-intercept.

g(x)=9-5x

CommutativePropAdd

Commutative Property of Addition

g(x)=- 5x+9

Now, let's graph these lines.

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

1/2x-2=9-5x

MultEqn

LHS * 2=RHS* 2

x-4=18-10x

AddEqn

LHS+10x=RHS+10x

11x-4=18

AddEqn

LHS+4=RHS+4

11x=22

DivEqn

.LHS /11.=.RHS /11.

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-2=9-5x

Substitute

x= 2

1/2( 2)-2? =9-5( 2)

Multiply

Multiply

1-2? =9-10

SubTerms

Subtract terms

- 1=- 1 ✓