Determine x:4 + x = 6 − x

The equation 4 + x = 6 − x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 − 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 = 1, which is not valid. The correct solution is the value that balances both sides of the equation. References/topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.

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