Question

Write the verbal sentence as an equation. Then tell whether 5 is a solution of the equation.

The product of 6 and x is 54.

Short answer

The equation is $6 · x = 54$andthe solution of the equation isnot5

Step-by-step solution

What is a variable?

A symbol we usually pick letters to be symbols, usually represents a number. Any letter you choose can be a variable.

How do you describe an Algebraic Expression? 

A variable is a symbol that stands in for an unknown value in a mathematical expression. A variable expression is a combination of terms and mathematical operations that contains at least one variable. Example a + 2x + 10

Apply the concept of equation: 

An equation is a mathematical statement that two expressions are equal. The solution of an equation is the value that when substituted for the variable makes the equation a true statement.

Example: 3x + 5 = 14 is an equation, in which 3x+5 and 14 are two expressions separated by an ‘’equal’’ sign.

Step 4: Write the verbal sentence as an equation. The product of 6 and x is 54.. Then tell whether 5 is a solution of the equation.

Converting the phrase into an equation:

In the left side, the phrase is ‘’the product of 6 and x’’. Product means the multiplication and x is the variable and the right side is 54.

Now we can write ‘‘’the product of 6 and x’’ is $6 · x$

The equation is $6 · x = 54$

Now solving the equation $6 · x = 54$with proper steps

$\begin{array}{l}6·x=54\\ \frac{6x}{6}=\frac{54}{6}\left[\text{Divideeachsideby}6\right]\\ x=9\end{array}$

Solution of the equation is$x = 9$

Solution is not 5, correct solution is x = 9