Question

Write and solve the equation for the sentence “The sum of one half of a number and 6 equals one third of the number.”

Short answer

The equation for the given problem is $\frac{1}{2}x+6=\frac{1}{3}x$.

The value of the number is $-36$.

Step-by-step solution

Step-1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Step-2. Concept of equation.

Equations: - Equations are the statements in which two expressions are equal. The expression can be created by variables, constants, numbers and symbols.

Step-3. Solution of the given problem.

The given problem is:

The sum of one half of a number and 6 equals one third of a number.

Let the number be x.

The given problem can be written in the form of an equation as

$\frac{1}{2}x+6=\frac{1}{3}x$

Add $-6-\frac{1}{3}x$to both sides of the equation.

$\begin{array}{l}\frac{1}{2}x+6-6-\frac{1}{3}x=\frac{1}{3}x-6-\frac{1}{3}x\\ \frac{1}{2}x-\frac{1}{3}x=-6\\ \frac{3-2}{6}x=-6\\ \frac{x}{6}=-6\end{array}$

Multiply 6 to both sides of the equation.

$\begin{array}{l}\left(6\right)\times -\frac{x}{6}=6\times \left(-6\right)\\ x=-36\end{array}$

Hence, the number is $-36$.