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Chapter 6: Problem 83

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(3-x=2 x+3\)

Short Answer

Expert verified
The unique solution to the given equation is \(x = 0\).

Step by step solution

01

Simplify the Equation

Firstly, collect like terms on both sides of the equation to simplify it: \(3 - x = 2x + 3\). This can be rewritten as \( -x - 2x = 3 - 3\).
02

Further Simplification

Further simplify the equation by combining like terms, resulting in: \(-3x = 0\).
03

Isolate the Variable x

To isolate \(x\), divide both sides of the equation by -3: \(x = 0/-3\).
04

Identify the Solution

Solving for \(x\), we find that \(x = 0\), which is a valid real number. Therefore, the equation has a unique solution.

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