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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Solving Equations by Graphing

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Exercise 5 Page 247

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

$x = - 3$

Practice makes perfect

To graph the equation

- x - 1 = \frac{1}{3} x + 3,

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

f (x) = - x - 1 and g (x) = \frac{1}{3} x + 3

The

x -

coordinate where the graphs of these functions intersect is the solution to our equation.

Point of intersection

The graphs intersect at

x = - 3,

which is our solution. We can verify this algebraically by solving the equation.

- x - 1 = \frac{1}{3} x + 3

$LHS \cdot 3 = RHS \cdot 3$

3 (- x - 1) = 3 (\frac{1}{3} x + 3)

▼

Simplify

Distribute $3$

3 (- x) - 3 (1) = 3 (\frac{1}{3} x) + 3 (3)

DenomMultFracToNumber

$3 \cdot \frac{a}{3} = a$

3 (- x) - 3 (1) = (1) x + 3 (3)

Identity Property of Multiplication

3 (- x) - 3 = x + 3 (3)

$a (- b) = - a \cdot b$

- 3 x - 3 = x + 3 (3)

Multiply

- 3 x - 3 = x + 9

$LHS - x = RHS - x$

- 4 x - 3 = 9

$LHS + 3 = RHS + 3$

- 4 x = 12

$LHS / (- 4) = RHS / (- 4)$

x = \frac{1 2}{- 4}

MoveNegDenomToFrac

Put minus sign in front of fraction

x = - \frac{1 2}{4}

Calculate quotient

x = - 3

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.

- x - 1 = \frac{1}{3} x + 3

$x = - 3$

- (- 3) - 1 = ? \frac{1}{3} (- 3) + 3

$- (- a) = a$

3 - 1 = ? \frac{1}{3} (- 3) + 3

$a (- b) = - a \cdot b$

3 - 1 = ? - 1 + 3

Add and subtract terms

2 = 2 ✓

Subchapter links

Communicate Your Answer p.243

Monitoring Progress p.244-246

Exercises p.247-248