Example Card: Solving an Absolute Value Equation with a Binomial
Master solving absolute value equations with binomials in Grade 9 algebra. Isolate |x+5|, split into two linear equations, and find both solutions step by step.
Key Concepts
This time, the absolute value holds a binomial. Don't worry, the strategy is the same. This problem illustrates our second key idea: solving for a more complex expression inside the absolute value bars.
Example Problem.
Solve the equation $4|x+5| 2 = 18$.
Common Questions
How do you solve an absolute value equation with a binomial?
Isolate the absolute value expression first, then split into two equations: one where the binomial equals the positive value and one where it equals the negative. Solve both for x.
What are the steps to solve 4|x+5| - 2 = 18?
Add 2 to both sides to get 4|x+5| = 20, divide by 4 to get |x+5| = 5, then split into x+5 = 5 (x=0) and x+5 = -5 (x=-10).
Why does solving an absolute value equation give two solutions?
Absolute value measures distance from zero, so both a positive and negative value can share the same absolute value, creating two separate equations to solve.