Unknowns on both sides
Solve 4x + 7 = x + 19
The aim is to get x on its own. Whatever we do to one side, we do to the other, so the equation stays balanced. This one takes 3 steps.
- 4x + 7 = x + 19The question.
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Step 1: Subtract x on both sides −x
There’s x on both sides. Take away x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.
3x + 7 = 19On the right, the x cancels out. Now there’s no x on the right.
You can add or take away x terms, just like numbers.
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Step 2: Subtract 7 on both sides −7
On the left, the x part has + 7 with it. Take 7 away from both sides to get rid of it.
3x = 12On the left, the 7 cancels out.
+ 7 is undone by − 7.
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Step 3: Divide by 3 on both sides ÷3
3x means 3 × x. Divide both sides by 3 to get x on its own.
x = 4x is on its own. x = 4.
Multiplying is undone by dividing.
Answer: x = 4
Check it
Put x = 4 back into the question. If both sides come to the same number, the answer is right.
Left side: 4x + 7 → 16 + 7 = 23
Right side: x + 19 → 4 + 19 = 23
✓ Both sides are 23, so x = 4 is right.
Now try it yourself
Solve this one in Algebra Balance. You choose each step, and it explains what happened, with hints if you get stuck.
Practise this in Algebra Balance