Question

Solve: 10 2/3+2h≤4 1/3

Answer 1

`\large\boxed{h\leq-(19)/(6)\to h\in\left(-\infty,\ -(19)/(6)\right]}`

Explanation:

`\text{First convert the mixed numbers to the improper fractions:}\\\\10(2)/(3)=(10\cdot3+2)/(3)=(32)/(3)\\\\4(1)/(3)=(4\cdot3+1)/(3)=(13)/(3)\\\\\text{Solve the inequality}\\\\10(2)/(3)+2h\leq4(1)/(3)\\\\(32)/(3)+2h\leq(13)/(3)\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot(32)/(3\!\!\!\!\diagup_1)+3\cdot2h\leq3\!\!\!\!\diagup^1\cdot(13)/(3\!\!\!\!\diagup_1)\\\\32+6h\leq13\qquad\text{subtract 32 from both sides}\\\\6h\leq-19\qquad\text{divide both sides by 6}\\\\h\leq-(19)/(6)`