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Big Ideas Math Integrated I, 2016 View details

5. Solving Equations by Graphing

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Exercise 6 Page 247

Create functions from the left-hand and right-hand sides of the equation.

$x = 2$

Practice makes perfect

To graph the equation

- \frac{3}{2} x - 2 = - 4 x + 3,

we will create two functions out of the left- and right-hand sides of the equation.

f (x) = - \frac{3}{2} x - 2 and g (x) = - 4 x + 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.

- \frac{3}{2} x - 2 = - 4 x + 3

MultEqn

$LHS \cdot 2 = RHS \cdot 2$

- 3 x - 4 = - 8 x + 6

AddEqn

$LHS + 8 x = RHS + 8 x$

5 x - 4 = 6

AddEqn

$LHS + 4 = RHS + 4$

5 x = 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.