Question

The difference between three times a number and five is equal to four times the number increased by two

Answer 1

Let the number be

`=x`

Three times a number will be

`\begin{gathered} =3* x \\ =3x \end{gathered}`

The difference between three times a number and five (5) will be

`=3x-5`

Four times the number is

`\begin{gathered} =4* x \\ =4x \end{gathered}`

Four times the number increased by two will be

`=4x+2`

By equating all the equations together, we will have

`3x-5=4x+2`

Step 1: Collect similar terms by subtracting 4x from both sides

`\begin{gathered} 3x-5=4x+2 \\ 3x-4x-5=4x-4x+2 \\ -x-5=2 \end{gathered}`

Step 2: Collect similar terms by adding 5 to both sides

`\begin{gathered} -x-5=2 \\ -x-5+5=2+5 \\ -x=7 \end{gathered}`

Step 3: Divide both sides by -1

`\begin{gathered} -x=7 \\ -(x)/(-1)=(7)/(-1) \\ x=-7 \end{gathered}`

Hence,

The number = -7