Solve: $\frac{y + 1}{2} - \frac{2y - 1}{3}$ = 4

Step 1: Analyze the question We need to find y in an equation with fractions. The strategy is to clear the fractions by multiplying through by the LCM of the denominators.

Step 2: Concept The LCM of 2 and 3 is 6. Multiplying every term by 6 removes the fractions. Be careful with the minus sign in front of the second fraction, because it applies to the whole bracket (2y − 1).

Step 3: Solution

(y + 1)/2 − (2y − 1)/3 = 4

Multiply through by 6:

3(y + 1) − 2(2y − 1) = 24

Expand:

3y + 3 − 4y + 2 = 24

Combine like terms:

−y + 5 = 24

−y = 19

y = −19

Check: Substitute y = −19.

• (−19 + 1)/2 = −18/2 = −9
• (2(−19) − 1)/3 = −39/3 = −13
• −9 − (−13) = −9 + 13 = 4 ✓

Step 4: Answer y = −19, which is option B.

Tip: When subtracting a fraction whose numerator has more than one term, put that numerator in brackets first, as in −2(2y − 1). Most students lose marks by forgetting to change the sign of the +1 inside the bracket. Always check your answer by substituting it back, since it takes only 30 seconds.