Big Ideas Math Algebra 1, 2015
BI
Big Ideas Math Algebra 1, 2015 View details
5. Solving Equations by Graphing
Continue to next subchapter

Exercise 3 Page 263

Break down the given absolute value equation into two separate equations.

x=- 4, x=0

Practice makes perfect

When solving an equation involving absolute value expressions, we should consider what would happen if we removed the absolute value symbols. Let's look at an example equation. |ax+b|=|cx+d| Although we can make 4 statements about this equation, there are actually only two possible cases to consider.

Statement Result
Both absolute values are positive. ax+b=cx+d
Both absolute values are negative. -(ax+b)=-(cx+d)
Only the left-hand side is negative. -(ax+b)=cx+d
Only the right-hand side is negative. ax+b=-(cx+d)
Because of the Properties of Equality, when the absolute values of two expressions are equal, either the expressions are equal or the opposites of the expressions are equal. Now let's consider these two cases for the given equation.

Given Equation:&& |2x+2|&=|x-2| First Equation:&& 2x+2&=x-2 Second Equation:&& 2x+2&=-(x-2) We will solve each of these equations by graphing separately.

First Equation

To graph the first equation, we will create two functions out of the left- and right-hand sides of the equation. y=2x+2 and y=x-2 The x-coordinate where the graphs of these functions intersect is the solution to our equation.

Point of intersection
From the graph, we can see that the graphs intersect at (- 4,- 6) which means the solution to the equation is x=- 4. Let's check whether it is correct by substituting it into the original equation.
|2x+2|=|x-2|
|2( - 4)+2|? =| - 4-2|
â–Ľ
Simplify
|- 8+2|? =|- 4-2|
|- 6|? =|- 6|
6=6 âś“
The equation is true, so x=- 4 solves the equation.

Second Equation

In order to graph the second equation, we will again create functions out of the left- and right-hand sides of the equation. y=2x+2 and y=-(x-2) Once more, the x-coordinate where the graphs of these functions intersect is the solution to our equation.

Point of intersection
From the graph, we can see that the lines intersect at (0,2), which means the solution to this equation is x=0.
|2x+2|=|x-2|
|2( 0)+2|? =| 0-2|
â–Ľ
Simplify
|2|? =|- 2|
2? =|- 2|
2=2 âś“
Since the equation is correct, x=0 is another solution to the equation.