Question

Which sentence represents the inequality 1/2x+3/4_>5 1/4?

Answer 1

`\large\boxed{x\geq9\to x\in\left[9,\ \infty\right)}`

Explanation:

`(1)/(2)x+(3)/(4)\geq5(1)/(4)\qquad\text{convert the mixed number to the improper fraction}\\\\(1)/(2)x+(3)/(4)\geq(5\cdot4+1)/(4)\\\\(1)/(2)x+(3)/(4)\geq(21)/(4)\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^2\cdot(1)/(2\!\!\!\!\diagup_1)x+4\!\!\!\!\diagup^1\cdot(3)/(4\!\!\!\!\diagup_1)\geq4\!\!\!\!\diagup^1\cdot(21)/(4\!\!\!\!\diagup_1)\\\\2x+3\geq21\qquad\text{subtract 3 from both sides}\\\\2x\geq18\qquad\text{divide both sides by 2}\\\\x\geq9`

<, > - open circle

≤, ≥ - closed circle

<, ≤ - draw the line to the left

>, ≥ - draw the line to the right