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

1 Answer
Nov 25, 2017

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.