Question

I need to solve for x and how many three-digit numbers is the above inequality true for

Answer 1

Given:

`(x)/(3)+(x)/(6)\ge(x)/(4)+230`

Required:

we have to calculate the above equation for the value of x.

Step-by-step explanation:

First of all we find common denominator

`\begin{gathered} (2x+x)/(6)\ge(x)/(4)+230 \\ \\ combine\text{ like terms} \\ (3x)/(6)\ge(x)/(4)+230 \end{gathered}`
`\begin{gathered} cancel\text{ terms that are in both numenator and denomenator} \\ (x)/(2)\ge(x)/(4)+230 \\ find\text{ common denominator} \\ (x)/(2)\ge(x)/(4)+\frac{4.230}{4\text{ }} \\ \\ (x)/(2)\ge(x+4.230)/(4) \\ \end{gathered}`
`\begin{gathered} multiply\text{ the numbers} \\ (x)/(2)\ge(x+920)/(4) \\ multiply\text{ all terms by the same value to eliminate fraction denominator.} \\ 4.(x)/(2)\ge4.(x+920)/(4) \\ cancel\text{ multiplies terms that are in denominator} \\ 2x\ge x+920 \\ subtract\text{ x from both the sides} \\ x\ge920 \end{gathered}`

Required answer:

`x\ge920`