Original independent learning guide. Not official KICD content.
Keep both sides equal
An equation states that two quantities have equal values. Adding, subtracting, multiplying or dividing both sides by the same suitable value preserves that equality. Division by zero is not permitted. For 5x minus 7 equals 18, add 7 to both sides to obtain 5x equals 25, then divide by 5 to obtain x equals 5. The operations explain the result more clearly than saying a number simply changes sides.
Worked example with brackets
Solve 3(x plus 2) equals 21. One method divides both sides by 3 first: x plus 2 equals 7, so x equals 5. Another expands the bracket to 3x plus 6 equals 21, subtracts 6 and divides by 3. Both methods give the same answer. Check by substituting 5 into the original expression: 3 times (5 plus 2) equals 21. Distribute multiplication to every term when expanding a bracket.
Translate a situation carefully
In an invented practice problem, three identical exercise books and a pen costing KSh 30 total KSh 180. Let b be the price of one book. The equation is 3b plus 30 equals 180, giving b equals 50. State the units and explain the assumption that the books have equal prices. These numbers describe a practice example, not SOMO product prices or a financial transaction. A useful model names what the variable means before manipulating symbols.
Prepare a correction log
Try one equation with brackets and one written situation before consulting answers. Record the first incorrect step, the operation that should replace it and a substitution check. Ask your teacher which current topics require these skills and which mathematics learning area you are taking. Use this refresher to identify a prerequisite gap rather than calling it an official Grade 10 examination. A correct final value without justified working may conceal a mistaken method.
Practice questions
Solve 4x plus 6 equals 30.
Solve 2(y minus 3) equals 14.
Two equal packets and 4 loose counters total 22. How many counters per packet?
Answers and explanations
Subtract 6 to get 4x = 24; divide by 4 to get x = 6.
Divide by 2: y minus 3 = 7. Add 3: y = 10. Check: 2 times (10 minus 3) = 14.
Let c be counters per packet. 2c + 4 = 22; 2c = 18; c = 9.