In the equation x + 10 = 22, what do you need to do to solve the problem?

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isabellacollier0413 isabellacollier0413

03-11-2026
Mathematics

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In the equation x + 10 = 22, what do you need to do to solve the problem?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T15:20:17-05:00

Identify that the equation \(x + 10 = 22\) involves adding 10 to the variable \(x\).
Recognize that the inverse operation of addition is subtraction.
State that to solve for \(x\), one must subtract 10 from both sides of the equation to maintain balance.
The final calculation leads to the solution: \(x = \boxed{12}\).

Explanation

Problem Analysis

The given equation is \(x + 10 = 22\). We have a variable \(x\) on the left-hand side, which is currently being increased by 10. To find the value of \(x\), we need to isolate it by itself on one side of the equation. This requires us to perform operations that undo the current state of the variable.

Identifying the Inverse Operation

The variable \(x\) is being added to 10. In algebra, we use inverse operations to isolate a variable. The inverse operation to addition is subtraction. Therefore, to remove the 10 from the left side of the equation, we need to subtract 10. To maintain the equality of the equation, whatever we do to one side, we must also do to the other side.

Conclusion

To isolate \(x\), we perform the subtraction of 10 from both sides of the equation. This is expressed as:
\[x + 10 - 10 = 22 - 10\]
By subtracting 10 from the left side, we are left with \(x\), and by subtracting 10 from the right side, we calculate the resulting value:
\[x = 12\]
Thus, the necessary step is to subtract 10 from both sides of the equation.

Examples

Think of an algebraic equation like a balance scale in a grocery store. If you put a bag of unknown weight \(x\) and a 10g weight on one side of the scale, and a 22g weight on the other side, the scale is perfectly balanced. To find the weight of the bag (\(x\)), you simply remove the 10g weight from the first side. To keep the scale balanced, you must also remove a 10g weight from the second side. After removing the weights, you are left with the bag of weight \(x\) on one side and a 12g weight on the other, confirming that \(x = 12\).