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Chapter 6: Problem 84

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(5-x=4 x+5\)

Short Answer

Expert verified
The solution to the equation is \(x = 0\), and the solution set in set notation is {0}.

Step by step solution

01

Combine like terms

First, group the terms with \(x\) together and the constants together. This gives us: \(5 - 5 = 4x + x\)
02

Simplify

Simplify the equation. On the left side, \(5 - 5 = 0\). On the right side, combine the \(x\) terms, \(4x + x = 5x\). This leaves us with \(0 = 5x\).
03

Solve for \(x\)

To solve for \(x\), divide both sides of the equation by 5. This gives us \(x = 0 / 5\).
04

Find the solution set

Finally, \(x = 0\). So, the solution set in set notation is {0}.

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