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Chapter 10: Chapter 10

Problem 186

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Solve the equation \(4 x-5=x+7\)

Short Answer

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The solution to the equation \(4x - 5 = x + 7\) is \(x = 4\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Move all terms with x to one side of the equation

Subtract \(x\) from both sides of the equation to collect the \(x\) terms on one side. This will give us: \[4x - 5 - x = x + 7 - x\] \[3x - 5 = 7\]

Step 2: Move all constant terms to the other side of the equation

To isolate x, we need to move the constant term (-5) to the other side of the equation. We do this by adding 5 to both sides: \[3x - 5 + 5 = 7 + 5\] \[3x = 12\]

Step 3: Divide both sides of the equation by the coefficient of x

Now, we need to find the value of x by dividing both sides of the equation by the coefficient of x (which is 3): \[\frac{3x}{3} = \frac{12}{3}\] \[x = 4\] So, the solution to the equation \(4x - 5 = x + 7\) is \(x = 4\).

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