Question

I need help with this work sheet. Put I already did E and A and L.

Answer 1

Given the expression:

`(5)/(6)(12k+30)\ge2k+17`

Step 1: Solve the expression by changing the fraction to whole number

`\begin{gathered} (5)/(6)(12k+30)\ge2k+17 \\ \text{ multiply through by 6} \\ 5(12k+30)\ge6(2k+17) \end{gathered}`

Step 2: Open the bracket

`\begin{gathered} 5(12k+30)\ge6(2k+17) \\ 60k+150\ge12k+102 \end{gathered}`

Step 3: Collect like terms

`\begin{gathered} 60k+150\ge12k+102 \\ 60k-12k\ge102-150 \\ 48k\ge-48 \\ \text{divide both side by 48} \end{gathered}`
`\begin{gathered} k\ge-(48)/(48) \\ k\ge-1 \end{gathered}`

Therefore the value of k is greater than or equal to -1

`k\ge-1`