Equations with negative numbers
Solve 23 − 4x = −17
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.
- 23 − 4x = −17The question.
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Step 1: Add 4x on both sides +4x
On the left, the x term is −4x, which is negative. Add 4x to both sides, so the x term is positive.
23 = −17 + 4xOn the left, the 4x cancels out. Now there’s no x on the left.
− 4x is undone by + 4x.
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Step 2: Add 17 on both sides +17
On the right, the x part has − 17 with it. Add 17 to both sides to get rid of it.
40 = 4xOn the right, the 17 cancels out.
− 17 is undone by + 17.
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Step 3: Divide by 4 on both sides ÷4
4x means 4 × x. Divide both sides by 4 to get x on its own.
10 = xx is on its own. x = 10.
Multiplying is undone by dividing.
Answer: x = 10
Check it
Put x = 10 back into the question. If both sides come to the same number, the answer is right.
Left side: 23 − 4x → 23 − 40 = −17
Right side: −17 → −17
✓ Both sides are −17, so x = 10 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