Given the inequality
[tex]19x+29\leq10x+83[/tex]
Subtract 10x on both sides.
[tex]\begin{gathered} 19x+29-10x\leq10x+83-10x \\ 9x+29\leq83 \end{gathered}[/tex]
Subtract 29 on both sides.
[tex]\begin{gathered} 9x+29-29\leq83-29 \\ 9x\leq54 \end{gathered}[/tex]
Divide by 9 on both sides.
[tex]x\leq\frac{54}{9}=6[/tex]
In interval notation, it can be written as
[tex](-\infty,6\rbrack[/tex]
