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Break down the given absolute value equation into two separate equations.
x=- 2 or x=1
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) |
Given Equation:& |x-4|=|3x| First Equation:& x-4 = 3x Second Equation:& x-4 =- 3x We will solve each of these equations by graphing separately.
To graph the first equation, we create two functions out of the left- and right-hand sides of the equation. y=x-4 and y=3x The x-coordinate of the point of intersection of the graphs of these functions is the solution to our equation.
In order to graph the second equation, we again create functions out of the left- and right-hand sides of the equation. y=x-4 and y=- 3x Once more, the x-coordinate where the graphs of these functions intersect is the solution to our equation.