Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 14 Equations

Linear equation with x on both sides

Answer: x = -4

💡 What it's asking: Gather all the x terms on one side and all the plain numbers on the other, then divide.

1. 1Take x from both sides so the x terms are together on the left: 3x − x.
2. 2Take 1 from both sides so the numbers are on the right: −7 − 1.
3. 3So 2x = −8.
4. 4Divide by 2: x = −4.

✅ Put x = −4 into both sides: 3(−4) + 1 = −11 and −4 − 7 = −11. They match.

Equation with two fractional terms

Answer: a = 12

💡 What it's asking: Fractions make equations messy. Multiply every term by the LCM of the denominators (the smallest number they both divide into) to clear them.

1. 1The denominators are 3 and 2; their LCM is 6.
2. 2Multiply every term by 6: 6 × a/3 = 2a, 6 × a/2 = 3a, and 6 × 10 = 60.
3. 3So 2a + 3a = 60, which is 5a = 60.
4. 4Divide by 5: a = 12.

✅ 12/3 + 12/2 = 4 + 6 = 10. Correct.