Question

Write and solve the equation for the sentence “Seven times a number equals $-84$.” What is the number?

Short answer

The equation for the given problem is $7x=-84$.

The value of the number is $-12$.

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:

Seven times a number equals $-84$.

Let the number be x.

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

$7x=-84$

Multiply $\frac{1}{7}$to both sides of the equation.

$\begin{array}{l}\frac{1}{7}\times 7x=-84\times \frac{1}{7}\\ x=-12\end{array}$

Therefore, the number is $-12$.