Original independent learning guide. Not official KICD content.
Collect like terms
Terms can be combined when their variable parts match. In 2x + 5x, both terms count the same kind of quantity, so their sum is 7x. In 2x + 5, the 5 is a constant and cannot be combined with 2x to make 7x. You can think of two identical bags plus five loose counters: the bags and counters are different units.
Worked example: solve 3x + 2 = 14
Subtract 2 from both sides to obtain 3x = 12. Then divide both sides by 3 to obtain x = 4. Each operation keeps the sides balanced. Check in the original equation: 3 × 4 + 2 = 14. This final check can catch an arithmetic error even when the chosen method was correct.
From words to an equation
Suppose three identical notebooks and a KSh 20 pen cost KSh 140 in a made-up practice problem. If x is the price of one notebook, write 3x + 20 = 140. Subtract 20 and divide by 3: x = 40. The answer is KSh 40 per notebook. Define the letter before writing the equation so that the units remain clear.
Avoid a common shortcut error
Changing a sign without knowing why can hide a mistake. Instead of saying a number simply moves across the equals sign, name the operation performed on both sides. Keep your working on separate lines. If your answer does not satisfy the original equation, locate the first line that is no longer equivalent.
Practice questions
Simplify 4a + 3a − 2.
Solve 2x + 7 = 19.
Five equal packets contain 35 counters altogether. Write and solve an equation for counters per packet.
Answers and explanations
The like terms give 7a − 2. The constant −2 remains separate.
Subtract 7: 2x = 12. Divide by 2: x = 6. Check: 2 × 6 + 7 = 19.
Let c be counters per packet. Then 5c = 35, so c = 7. Each packet contains seven counters.
