Algebra 4

4 marks · Hard

Solve the equation . Show all your working.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

x = 1

Common mistakes: Adding fractions incorrectly, leading to wrong common denominator.; Mishandling bracket signs.

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Multiplies both sides by the lowest common denominator (12) or equivalent approach.

M2 · 1 mark · Expands and collects like terms to form a correct linear equation in x. (follow-through)

A1 · 1 mark · Correctly solves for x from the simplified equation. (follow-through)

A2 · 1 mark · Gives the correct final value for x: x = 1. (follow-through)

Worked solution

Multiply both sides by 12 (lowest common denominator):

That gives:

Expand and collect terms:

Rechecking: this answer is , but let's check for accuracy—there was an error. Let's start afresh.

Rewrite the fractions with a common denominator of 12:

So:

Multiply both sides by 12:

So the correct answer is .