Question

How do you solve `11x + 8y \geq 56`?

Answer 1

Since your question is a little unclear, I will give you the following answers.

If you want to solve for `x`, then `x>=(56-8y)/11`

If you want to solve for `y`, then `y>=-11/8x+7`

If you were to graph it, then color in the right side of the graph. graph{-11/8x+7 [-14.24, 14.23, -7.12, 7.12]}

Explanation:

To solve the inequality for either `x` or `y`, you would use the inverse operation.

You would do the following:
For `x`:
`11x+8y-8y>=56-8y`
`(11x)/11>=(56-8y)/11`
`x>=(56-8y)/11`
`x>=-8/11y+56/11`

For `y`:
`11x-11x+8y>=56-11x`
`(8y)/8>=(56-11x)/8`
`y>=-11/8x+7`

To graph the inequality, use the solution for `y.`

First, graph the equation `y=-11/8x+7` which should look like this:
graph{-11/8x+7 [-10, 10, -5, 5]}

Now, pick an `x` value (say, 10). Then, plug the number in the inequality.

`-11/8xx10+7=-6.75`

For the inequality to hold true, we want the y values for the particular x value to be greater than -6.75. All the y values that are located to the right side of the slope will make the inequality true. Therefore, color the right side of the slope.