Question

Solve the inequality.
3x+6<3(x-7)

Answer 1

0 < - 27

Explanation:

1. Distribute

3x + 6 < 3(x-7)

3x + 6 < 3x - 21

2. Subtract 6 from both sides

3x + 6 < 3x - 21

3x + 6 - 6 < 3x - 21 - 6

3. Simplify

subtract

3x + 6 - 6 < 3x - 21 - 6

3x < 3x - 21 - 6

subtract

3x < 3x - 21 - 6

3x < 3x - 27

4. Subtract 3x from both sides

3x < 3x - 27

3x - 3x < 3x - 27 - 3x

5. Simplify

combine like terms

3x - 3x < 3x - 27 - 3x

0 < 3x - 27 - 3x

0 < 3x - 27 - 3x

0 < - 27

And that is how you get your answer

Answer 2

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3(x-7) } \end{gathered}$} }`

Simplify both sides of the inequality.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3x-21 } \end{gathered}$} }`

Subtract 3x from both sides.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6-3x < 3x-21-3x } \end{gathered}$} }`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{6 < -21 } \end{gathered}$} }`

Subtract 6 from both sides.

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{6-6 < -21-6 } \end{gathered}$} }`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{0 < -27} \end{gathered}$} }`

There are no solutions.

Standard form: x ∈ ∅