Question

Solve for p. write your answer with p first followed by an inequality symbol

Answer 1

We can add the two similar terms on the right side of the inequality:

`\begin{gathered} -19p-10\ge12-14p-7p \\ \Rightarrow-19p-10\ge12-21p \end{gathered}`

now we can move all the terms with p to the left side of the inequality, and all the constants to the right side:

`\begin{gathered} -19p-10\ge12-21p \\ \Rightarrow-19p+21p\ge12+10 \\ \Rightarrow2p\ge22 \end{gathered}`

since the coefficient of the term 2p is positive, we can move it to the opposite side dividing without changing the inequality sign:

`\begin{gathered} 2p\ge22 \\ \Rightarrow p\ge(22)/(2)=11 \\ \Rightarrow p\ge11 \end{gathered}`

therefore, p is greater or equal to 11