How do you solve #root3(4x)+11=5#?

Question

Eva Abramson · Accepted Answer

The answer is #x=-54#

This is how you approach resolving the issue:

#1.# The goal in questions like this is to isolate the variable you're trying to solve for.

#2.# So we start with subtracting #11# from both sides, so you get:

#root(3)4x =-6#

#3.# The next step is to get rid of the cube root. the way to do that is simply by raising both sides to the power of 3. notice that you canNOT simply go ahead and divide both sides by 4 and THEN get rid of the cube root. That is because #4x# is under the cube root and you should "free up the #4x#" from the cube root before you can divide by #4#. be aware of that so here is what it will look like:

#(root(3)4x)^3 =(-6)^3#

#4x = (-6)^3#

#4x = -216#

#4.# Finally we divide both sides by 4 to get #x# by itself:

#x = -216/4#

#x = -54#

I hope this was useful (c:

Kennedy Adams · Answer

undefined To solve the equation √3(4x) + 11 = 5, we can follow these steps:

1. Start by subtracting 11 from both sides of the equation: √3(4x) = -6.

2. Divide both sides of the equation by √3: 4x = -6/√3.

3. Rationalize the denominator by multiplying both the numerator and denominator by √3: 4x = -6√3/3.

4. Simplify the expression on the right side: 4x = -2√3.

5. Finally, divide both sides of the equation by 4 to isolate x: x = -2√3/4.

Therefore, the solution to the equation √3(4x) + 11 = 5 is x = -2√3/4.