Problem 93 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

\(x = 8\)

Step 1: 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 \(2x+28=52-x\).

Step 2: 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 \(3x = 24\).

Step 3: Solve for x

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