Respuesta :
Let the number be
[tex]=x[/tex]Three times a number will be
[tex]\begin{gathered} =3\times x \\ =3x \end{gathered}[/tex]The difference between three times a number and five (5) will be
[tex]=3x-5[/tex]Four times the number is
[tex]\begin{gathered} =4\times x \\ =4x \end{gathered}[/tex]Four times the number increased by two will be
[tex]=4x+2[/tex]By equating all the equations together, we will have
[tex]3x-5=4x+2[/tex]Step 1: Collect similar terms by subtracting 4x from both sides
[tex]\begin{gathered} 3x-5=4x+2 \\ 3x-4x-5=4x-4x+2 \\ -x-5=2 \end{gathered}[/tex]Step 2: Collect similar terms by adding 5 to both sides
[tex]\begin{gathered} -x-5=2 \\ -x-5+5=2+5 \\ -x=7 \end{gathered}[/tex]Step 3: Divide both sides by -1
[tex]\begin{gathered} -x=7 \\ -\frac{x}{-1}=\frac{7}{-1} \\ x=-7 \end{gathered}[/tex]Hence,
The number = -7
