Abs. Eq. with Coefficient
About this exercise
Equations where a whole expression lives inside the absolute-value bars.
Example problems
A few of the problems this exercise asks. The printable worksheet holds ten fresh ones.
- |2x − 7| = 3. Larger x?
- |2x + 1| = 5. Larger x?
- |2x + 2| = 10. Larger x?
- |2x + 6| = 8. Larger x?
Try it yourself first — open a section below only if you get stuck.
How to solve it
The bars hide the sign of what is inside, so the expression could equal the right-hand side or its negative. Write both versions, solve each as an ordinary linear equation, and keep both answers unless the question picks one.
Worked example
From |2x + 4| = 6 the two versions are 2x + 4 = 6 and 2x + 4 = -6, so x = 1 or x = -5, and the larger is 1.
Common mistake
Solving only the positive branch. The negative branch produces the second solution, and these questions often ask precisely for it.