Question

Solve for n: -3(1+4n)-6n ≤ 2n-23Graph the solution on a number line.

Answer 1

n≥1

Step-by-step explanation:

Given the inequality

`-3\mleft(1+4n\mright)-6n\le2n-23​`

Step 1: Open the bracket and simplify

`\begin{gathered} -3-12n-6n\le2n-23​ \\ -3-18n\le2n-23 \end{gathered}`

Step 2: Add 18n to both sides of the inequality.

`\begin{gathered} -3-18n+18n\le2n+18n-23 \\ -3\le20n-23 \end{gathered}`

Step 3: Add 23 to both sides of the inequality.

`\begin{gathered} -3+23\le20n-23+23 \\ 20\le20n \end{gathered}`

Step 4: Divide both sides of the inequality by 20.

`\begin{gathered} (20)/(20)\le(20n)/(20) \\ 1\le n \\ \implies n\ge1 \end{gathered}`