Exercise 12 Page 247

To graph the equation - 5+ 14x=3x+6, we will create two functions out of the left- and right-hand sides of the equation. f(x)=- 5+1/4x 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)=- 5+1/4x

CommutativePropAdd

Commutative Property of Addition

f(x)=1/4x-5

Now, let's graph these lines.

The graphs intersect at x=- 4, which is our solution. We can verify this algebraically by solving the equation.

- 5+1/4x=3x+6

MultEqn

LHS * 4=RHS* 4

- 20+x=12x+24

SubEqn

LHS-x=RHS-x

- 20=11x+24

SubEqn

LHS-24=RHS-24

- 44=11x

DivEqn

.LHS /11.=.RHS /11.

- 4=x

RearrangeEqn

Rearrange equation

x=- 4

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.

- 5+1/4x=3x+6

Substitute

x= - 4

- 5+1/4( - 4)? =3( - 4)+6

MultPosNeg

a(- b)=- a * b

- 5-1? =- 12+6

AddSubTerms

Add and subtract terms

- 6=- 6 ✓