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Chapter 2: Problem 93

Solve for \(x: \frac{x}{2}+7=13-\frac{x}{4}\) (Section \(2.3,\) Example 4 )

Short Answer

Expert verified
\(x = 8\)

Step by step solution

01

Eliminate Fractions

To make the equation easier to challenge, let's first clear the fractions by multiplying every term by the common denominator, which in this case is 4. This gives: \(4(\frac{x}{2}+7)=4(13-\frac{x}{4})\), which simplifies to \(2x+28=52-x\).
02

Isolate the variable

Now, it's easier to solve for \(x\). First, add \(x\) to both sides of the equation to keep it balanced. This results in \(2x + x = 52 - 28\), which simplifies to \(3x = 24\).
03

Solve for x

Now, divide both sides of the equation by 3 to solve for \(x\). This gives \(x = \frac{24}{3}\).

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