Equations with negative numbers
Solve 13 − 6x = −41
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.
- 13 − 6x = −41The question.
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Step 1: Add 6x on both sides +6x
On the left, the x term is −6x, which is negative. Add 6x to both sides, so the x term is positive.
13 = −41 + 6xOn the left, the 6x cancels out. Now there’s no x on the left.
− 6x is undone by + 6x.
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Step 2: Add 41 on both sides +41
On the right, the x part has − 41 with it. Add 41 to both sides to get rid of it.
54 = 6xOn the right, the 41 cancels out.
− 41 is undone by + 41.
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Step 3: Divide by 6 on both sides ÷6
6x means 6 × x. Divide both sides by 6 to get x on its own.
9 = xx is on its own. x = 9.
Multiplying is undone by dividing.
Answer: x = 9
Check it
Put x = 9 back into the question. If both sides come to the same number, the answer is right.
Left side: 13 − 6x → 13 − 54 = −41
Right side: −41 → −41
✓ Both sides are −41, so x = 9 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