Given the expression:
[tex]\frac{5}{6}(12k+30)\ge2k+17[/tex]
Step 1: Solve the expression by changing the fraction to whole number
[tex]\begin{gathered} \frac{5}{6}(12k+30)\ge2k+17 \\ \text{ multiply through by 6} \\ 5(12k+30)\ge6(2k+17) \end{gathered}[/tex]
Step 2: Open the bracket
[tex]\begin{gathered} 5(12k+30)\ge6(2k+17) \\ 60k+150\ge12k+102 \end{gathered}[/tex]
Step 3: Collect like terms
[tex]\begin{gathered} 60k+150\ge12k+102 \\ 60k-12k\ge102-150 \\ 48k\ge-48 \\ \text{divide both side by 48} \end{gathered}[/tex][tex]\begin{gathered} k\ge-\frac{48}{48} \\ k\ge-1 \end{gathered}[/tex]
Therefore the value of k is greater than or equal to -1
[tex]k\ge-1[/tex]
