Porisma

Worked solution

Compare two moduli using a difference or two graphs

Solve ∣1−2x∣>∣x+3∣|1-2x|>|x+3|.

CJC · Lecture · Example 9

Method 1: graph one difference

Rewrite as ∣1−2x∣−∣x+3∣>0|1-2x|-|x+3|>0. Sketch the piecewise-linear difference; its roots are −2/3 and 4. It is positive outside those roots, giving x<−2/3 or x>4.

How did this part go?

Method 2: compare the original V graphs

Sketch y=|1−2 x| and y=|x+3|. Their intersection inputs are −2/3 and 4. The first graph lies above the second for x<−2/3 or x>4. Equality at the crossings is excluded.

How did this part go?

Compare your sketch

Expand diagram

Use the scrollbars or arrow keys to inspect details.

Both source representations retain the piecewise-linear shapes, crossings −2/3 and 4 and strict outside solution x<−2/3 or x>4.
Both source representations retain the piecewise-linear shapes, crossings −2/3 and 4 and strict outside solution x<−2/3 or x>4.
Both source representations retain the piecewise-linear shapes, crossings −2/3 and 4 and strict outside solution x<−2/3 or x>4.

Common mistakes

Removing the modulus bars without choosing the correct linear branches changes the comparison.

Read the hint