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Chapter 6: Problem 76

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(3(x-1)=8 x+6-5 x-9\)

Short Answer

Expert verified
The equation is true for all real numbers.

Step by step solution

01

Simplify Left hand Side of Equation

The equation is \(3(x-1)=8 x+6-5 x-9\). Start by multiplying the term 3 with each term inside the parentheses on the left side of the equation. This simplifies \(3(x-1)\) to \(3x-3\)
02

Simplify Right hand Side of Equation

Combine the like terms on the right hand side of the equation. This combines \(8x-5x\) to \(3x\) and combines \(6-9\) to \(-3\) and as a result, we get \(3x-3\) on the right side of the equation
03

Compare Left and Right side of Equation

Now both sides of equation are equal, i.e \(3x-3=3x-3\). This implies that all real numbers are a solution, because no matter what value of 'x' you choose, the equation will hold true.

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