Question

Could you help me translate and solve an equation that matches the description below?11 less than 3 times a number is the same as 75 less than the product of -1 and the number.

Answer 1

-16

Explanation:

Given the statement:

11 less than 3 times a number is the same as 75 less than the product of -1 and the number.

We want to translate and solve the resulting equation for the number.

To begin with, let the number = x.

First Part: 11 less than 3 times a number

`\begin{gathered} 3\text{ times the number}=3x \\ 11\text{ less than }3\text{ times the number}=3x-11 \end{gathered}`

Second Part: 75 less than the product of -1 and the number.

`\begin{gathered} \text{Product of -1 and the number }=-x \\ 75\text{ less than product of -1 and the number }=-x-75 \end{gathered}`

Since we are told that the two statements are the same;

`\implies3x-11=-x-75`

We then solve the equation for the number, x.

`\begin{gathered} 3x-11=-x-75 \\ \text{Add x to both sides} \\ 3x+x-11=-x+x-75 \\ 4x-11=-75 \\ \text{Add 11 to both sides} \\ 4x-11+11=-75+11 \\ 4x=-64 \\ \text{Divide both sides by 4} \\ (4x)/(4)=-(64)/(4) \\ x=-16 \end{gathered}`

The number is -16.