Level 4 · Ages 13–15
Read it again any time, including while you work through the exercises.
Imagine a two pan scale in perfect balance. On the left pan: two identical mystery bags and a 3 kg weight. On the right pan: an 11 kg weight. How much does each bag weigh? You have just met the equation 2x + 3 = 11, where x is the mass of one bag.
An equation is an equality containing an unknown number, often called x. Solving the equation means finding the value or values of x that make the equality true. The golden rule comes from the scale: whatever you do on one side, you must also do on the other, otherwise the balance breaks.
The strategy is always the same: isolate x step by step. First remove what is added or subtracted (take 3 kg off each pan: 2x = 8), then deal with what multiplies (split each pan in 2: x = 4). Each bag weighs 4 kg.
Last champion reflex: check! Replace x with your solution in the original equation. Here: 2 × 4 + 3 = 11. Great, the equality is true. This check takes only a few seconds and catches almost every mistake.
Solve the equation 2x + 3 = 11.
2x + 3 - 3 = 11 - 3
I take 3 away from both sides so that 2x stays alone on the left.
2x = 8
The scale is still balanced: two bags weigh 8 kg.
x = 8 ÷ 2 = 4
I divide both sides by 2 to find one bag.
2 × 4 + 3 = 11
I check in the original equation: 8 + 3 = 11, we win!
Result: The solution is x = 4.
Solve the equation 5x - 4 = 2x + 8 (x on both sides).
5x - 2x - 4 = 8
I remove 2x from both sides to gather all the x on the left.
3x - 4 = 8 puis 3x = 12
I add 4 to both sides: the plain numbers move to the right.
x = 12 ÷ 3 = 4
I divide by 3 to isolate x.
5 × 4 - 4 = 16 et 2 × 4 + 8 = 16
Check: both sides equal 16, the equality is true.
Result: The solution is x = 4.