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Ages 12-14

Linear equations

Find the number hiding behind the x

What is this about?

An equation is a balanced scale: what's on the left of the = weighs the same as what's on the right. The x is a hidden number, and solving the equation means discovering it. The golden rule of the scale: whatever you do on one side, you must also do on the other to keep it balanced.

The rule to remember

Get the x alone step by step, undoing the operations in reverse order: first remove what adds or subtracts (doing the opposite operation on both sides) and then remove what multiplies or divides. At the end, check by substituting your result into the original equation.

Example 1

x + 7 = 12

  1. 1The x has a spare +7 next to it. To remove it, subtract 7 on BOTH sides.
  2. 2Left: x + 7 − 7 = x. Right: 12 − 7 = 5.
  3. 3That leaves x = 5.
  4. 4Check: 5 + 7 = 12. ✓ Correct.

Result: 5

Example 2

2x + 3 = 11

  1. 1First remove the +3: subtract 3 on both sides and you get 2x = 8.
  2. 2Now the x is multiplied by 2. To undo it, divide both sides by 2.
  3. 3That leaves x = 8 ÷ 2 = 4.
  4. 4Check: 2 × 4 + 3 = 11. ✓ Correct.

Result: 4

The most common mistake

Many people write

x + 5 = 12 → x = 12 + 5 = 17

Why it's wrong

When moving the 5 to the other side, its sign wasn't changed. If it was ADDING on the left, it goes to the right SUBTRACTING: x = 12 − 5 = 7. Check it: 7 + 5 = 12, while 17 + 5 = 22, which is not 12.

Did it click?

The best way to find out is to try. These exercises are exactly on this topic.

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