Answer:
1/3
Step-by-step explanation:
When working with balanced expressions (stuff on both sides of the equal sign), "what you do to one side, you do to the other", which keeps it balanced.
The first thing we notice is the exponent 1/4, which is one both sides, so we can get rid of it on both sides by using the <u>reverse operation</u>.
The reverse of exponents is <u>square root</u>.
![(4x + 10)^{\frac{1}{4}} = (9 + 7x)^{\frac{1}{4}}\\\sqrt[\frac{1}{4}]{(4x + 10)^{\frac{1}{4}}} = \sqrt[\frac{1}{4}]{(9 + 7x)^{\frac{1}{4}}}\\\\4x + 10 = 9 + 7x](https://tex.z-dn.net/?f=%284x%20%2B%2010%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20%3D%20%289%20%2B%207x%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5Csqrt%5B%5Cfrac%7B1%7D%7B4%7D%5D%7B%284x%20%2B%2010%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%20%3D%20%5Csqrt%5B%5Cfrac%7B1%7D%7B4%7D%5D%7B%289%20%2B%207x%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%5C%5C%5C%5C4x%20%2B%2010%20%3D%209%20%2B%207x)
Isolate x to solve. Separate the variables and non-variables.
4x + 10 = 9 + 7x
4x - 4x + 10 = 9 + 7x - 4x Subtract 4x from both sides
10 = 9 + 3x
10 - 9 = 9 - 9 + 3x Subtract 9 from both sides
1 = 3x Divide both sides by 3 to isolate x
x = 1/3 Answer
Answer:
6.84 ≤ x ≤ 37.39
Step-by-step explanation:
we have
-----> equation A
we know that
The company wants to keep its profits at or above $225,000,
so
-----> inequality B
Remember that P(x) is in thousands of dollars
Solve the system by graphing
using a graphing tool
The solution is the interval [6.78,39.22]
see the attached figure
therefore
A reasonable constraint for the model is
6.84 ≤ x ≤ 37.39
Answer:
228.6
Step-by-step explanation: