L5 · Simplifying both sides of an equation

Learning goal

“I can simplify each side of an equation separately - combining like terms and evaluating number-only parts on that side - so the equation is ready to solve, without changing what the equation says.”

Equation — a statement that two expressions are equal, with an equals sign: 5x + 3 = 18.

Side — everything on one side of the equals sign: the left side or the right side.

Balance — the picture of an equation as a scale: both sides must stay equal, so each side is tidied on its own tray.

Simplify (a side) — rewrite one side by combining its like terms and evaluating its number-only parts, without touching the other side.

Worked example

Simplify the left side of 4 + 3x + 2 = 24. Step 1: Work ONLY on the left tray. Sort its terms: x-terms (3x) and constants (4, 2). Step 2: Combine the constants: 4 + 2 = 6. The left side becomes 3x + 6. Step 3: The equation now reads 3x + 6 = 24. The right side was never touched. On the balance, the left tray held a 4-block, an x-bundle, and a 2-block; the two blocks are stacked into one 6-block - same total weight, the beam never moved. Simplifying a side tidies that side's OWN terms; nothing crosses the equals sign in this lesson.

Check yourself — explain it

Simplifying one side of an equation means...

Paired problem — example still visible

Simplify the left side: 7y - 2y = 15 -> 5y = 15

Faded completion — last step is yours

"6 + 4m + 2m = 30 simplifies to ___m + 6 = 30" -> 6

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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