Question

Solve the inequality. 14 + 10y ≥ 3(y + 14)

Answer 1

$\large\displaystyle\begin{gathered}\sf \bf{14+10y\geq 3(y+14) } \end{gathered}$

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{\sf{Simplify \ both \ sides \ of \ the \ inequality. }} \end{gathered} }$

• $\large\displaystyle\begin{gathered}\sf \bf{10y+14\geq 3y+14 } \end{gathered}$

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{\sf{Subtract \ 3y \ from \ both \ sides. }} \end{gathered} }$

• $\large\displaystyle\begin{gathered}\sf \bf{10y+14-3y\geq 3y+42-3y } \end{gathered}\\\large\displaystyle\begin{gathered}\sf \bf{7y+14\geq 41 } \end{gathered}$

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{\sf{ Subtract \ 14 \ from \ both \ sides. }} \end{gathered} }$

• $\large\displaystyle\begin{gathered}\sf \bf{7y+14-14\geq 42-14 } \end{gathered}\\\large\displaystyle\begin{gathered}\sf \bf{7y\geq 28 } \end{gathered}$

$\large\displaystyle\text{ \begin{gathered}\sf \boldsymbol{\sf{Divide \ both \ sides \ by \ 7. }} \end{gathered} }$

• $\large\displaystyle\text{ \begin{gathered}\sf \bf{\frac{7y}{7}\geq \frac{28}{7} } \end{gathered} }\\\boxed{\large\displaystyle\begin{gathered}\sf \bf{y\geq 4} \end{gathered} }$