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Chapter 6: Problem 79

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(4 x+1-5 x=5-(x+4)\)

Short Answer

Expert verified
The solution set for the given equation is the set of all real numbers, \(\mathbb{R}\).

Step by step solution

01

Simplify each side of the equation

First, combine like terms on both sides of the equation separately. The left side, \(4x+1-5x\), simplifies to \(-x+1\). The right side, \(5-(x+4)\), simplifies to \(1-x\). The equation is now \(-x+1=1-x\).
02

Solve the equation

Next, get all terms involving \(x\) on one side of the equation and the constants on the other side. Adding \(x\) to both sides will eliminate \(x\) from the left side, and the equation simplifies to \(1=1\). This is always true, regardless of the value of \(x\).
03

Express the solution set in set notation

Since the equation is true for all real numbers, the solution set is the set of all real numbers, denoted by \(\mathbb{R}\).

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