Exercise 14 Page 247

To graph the equation - 6(x+4)=- 3x-6, we will create two functions out of the left- and right-hand sides of the equation. f(x)=- 6(x+4) and g(x)=- 3x-6 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.

f(x)=- 6(x+4)

Distr

Distribute - 6

f(x)=- 6x-24

Now, let's graph these lines.

The graphs intersect at x=- 6, which is our solution. We can verify this algebraically by solving the equation.

- 6(x+4)=- 3x-6

Distr

Distribute - 6

- 6x-24=- 3x-6

AddEqn

LHS+3x=RHS+3x

- 3x-24=- 6

AddEqn

LHS+24=RHS+24

- 3x=18

DivEqn

.LHS /(- 3).=.RHS /(- 3).

x=- 6

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.

- 6(x+4)=- 3x-6

Substitute

x= - 6

- 6( - 6+4)? =- 3( - 6)-6

AddTerms

Add terms

- 6(- 2)? =- 3(- 6)-6

MultNegNegOnePar

- a(- b)=a* b

12? =18-6

SubTerm

Subtract term

12=12 ✓