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Chapter 10: Chapter 10

Problem 184

Next question

Solve \(3 \mathrm{x}-5=4\) for \(\mathrm{x}\)

Short Answer

Expert verified
The solution to the equation \(3x-5=4\) is \(x = 3\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify the equation and the variable to solve for

The equation given is \(3x-5=4\), and we want to solve for the variable \(x\).

Step 2: Add 5 to both sides of the equation

To start isolating the variable x, add 5 to both the left and right sides of the equation: \[3x - 5 + 5 = 4 + 5\] This simplifies to: \[3x = 9\]

Step 3: Divide both sides of the equation by 3

To completely isolate the variable x, divide both sides of the equation by 3: \[\frac{3x}{3} = \frac{9}{3}\] This simplifies to: \[x = 3\]

Step 4: Check the solution

To make sure that the solution is correct, plug the value of x back into the original equation: \[3(3) - 5 = 4\] \[(9 - 5) = 4\] \[4 =4\] Since both sides of the equation are equal, the solution is verified. Thus, the solution to the equation \(3x-5=4\) is \(x = 3\).

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