AlgebraAdditional / Further Maths

Solving absolute value / modulus equations

Solve an absolute value equation using two cases, then check each candidate.

  • The value inside the absolute value bars can equal the right side or its negative. Solve both cases.
  • For , try and . If is an expression, negate the whole expression.
  • Substitute each candidate into the original equation. Accept it only when both sides are equal.

Example 1

Solve the equation.

Case 1

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept

Case 2

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept

Example 2

Solve the equation.

Case 1

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Reject

Case 2

Expand the brackets and collect like terms.Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept

Remember
Absolute value is always non-negative. A candidate that makes the right side negative must be rejected.

Your turn

Question 1

Solve the equation. Check each candidate in the original equation.

Check answer

Case 1

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept

Case 2

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept
Question 2

Solve the equation. Check each candidate in the original equation.

Check answer

Case 1

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept

Case 2

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept
Question 3

Solve the equation. Check each candidate in the original equation.

Check answer

Case 1

Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Reject

Case 2

Expand the brackets and collect like terms.Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept
Question 4

Solve the equation. Check each candidate in the original equation.

Check answer

Case 1

Apply this to both sides.

Check in the original equation

Left side
Right side
Accept

Case 2

Expand the brackets and collect like terms.Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Accept
Question 5

Solve the equation. Check each candidate in the original equation.

Check answer

Case 1

Apply this to both sides.

Check in the original equation

Left side
Right side
Reject

Case 2

Expand the brackets and collect like terms.Apply this to both sides.Apply this to both sides.Simplify the numerical terms and collect like terms.

Check in the original equation

Left side
Right side
Reject
No solution
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