Equations with absolute values in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Solve the equation (lvert 3x-7lvert=-8 ).

Exercise 2.

Solve the equation ( lvert2x-4lvert-lvert x-1lvert=3 ).

Exercise 3.

Solve the equation (vert x-1vert=-4+2x).

Discussion

In Exercise 2, we propose a method. Instead, try to use a different approach: transform the equation in an equality between two positive quantities, take their square, etc.: which is your favorite method?