Chapter 9.7, Problem 7MRE

To determine

To simplify: the expression $\frac{x+4}{3}-\frac{x}{4}=\frac{2}{3}$ .

Answer to Problem 7MRE

The value is $x=\frac{8}{3}$ .

Explanation of Solution

Given information:

  $\frac{x+4}{3}-\frac{x}{4}=\frac{2}{3}$

Formula used:

Order of operations:

Step 1. Evaluate expressions inside grouping symbols.

Step 2. Evaluate all powers.

Step 3. Multiply and / or divide from left to right.

Step 4. Add and/or subtract from left to right.

Calculation:

Consider ,

  $\frac{x+4}{3}-\frac{x}{4}=\frac{2}{3}$

Taking L.C.M we get,

  $\begin{array}{l}=\left(\frac{x+4}{3}\times \frac{4}{4}\right)-\left(\frac{x}{4}\times \frac{3}{3}\right)=\frac{2}{3}\\ =\left(\frac{4(x+4)}{12}\right)-\left(\frac{3x}{12}\right)=\frac{2}{3}\\ =\left(\frac{4x+16}{12}\right)-\left(\frac{3x}{12}\right)=\frac{2}{3}\\ =\frac{4x+16-3x}{12}=\frac{2}{3}\\ =\frac{x+16}{12}=\frac{2}{3}\\ \end{array}$

  $\begin{array}{l}\text{cross-multiplying we get},\\ =3(x+16)=2(12)\\ =3x+16=24\\ \text{Subtracting}16\text{ from both the sides}\\ =3x+16-16=24-16\\ =3x=8\\ \text{Dividing both sides by }3\\ =\frac{3x}{3}=\frac{8}{3}\\ =x=\frac{8}{3}\end{array}$

Hence, the value is $x=\frac{8}{3}$ .