Absolute Value Worksheets

Three modes

Evaluate asks for the value of |x|, and of expressions combining two of them. Compare puts a symbol between two absolute values. Solve gives equations of the form |x| = k or |x ± a| = k and wants every solution.

Twenty questions by default with an answer key.

Distance from zero

That is the definition to teach, and it is better than "make it positive" for one specific reason: the shortcut fails the moment a variable is involved.

|−7| is 7 because −7 sits seven units from zero. |7| is also 7. Distance has no direction, which is exactly why the answer is never negative — and a pupil who has the distance picture will never write |x| = −3 has a solution.

Solving is where it gets interesting

|x| = 5 has two solutions, not one. Both 5 and −5 are five units from zero.

Missing the second solution is the defining error of this topic, and it persists. Insist that every solve answer is checked for a partner — if the equation gives a positive value on the right, there are always two, and if it gives a negative one there are none at all.

|x − 3| = 5 works the same way once you see the bars as asking about a distance: x is five units from 3, so x is 8 or −2. Splitting it into two equations, x − 3 = 5 and x − 3 = −5, is the mechanical route and it is worth teaching alongside the picture, because the mechanical route survives into inequalities.

Comparison mode

Quick, and it does something the others do not: it forces a pupil to evaluate before deciding, which catches anyone treating the bars as decoration.

|−9| against |4| looks like it should favour the 4 to a pupil reading signs rather than magnitudes. Enough of these and the habit breaks.

No solution is an answer

|x| = −2 has none. Some pupils will write 2, some will write −2, some will leave it blank because it looks broken.

Leaving it blank is closest to right, and "no solution" is the answer wanted. It is worth including deliberately, because it is the question that shows whether the definition landed or only the procedure did.

Level

Usually first met around thirteen or fourteen, alongside inequalities and coordinate geometry, and revisited when absolute value inequalities arrive.

Related: negative numbers, which this depends on entirely, and inequalities.