Solve each equation. See Example 7. (3x+7)^1/3-(4x+2)^1/3=0

Question

Accepted Answer

Hello, today we're gonna be solving for X in the given equation. So what we are given is six X plus 11 race to the power of 1/3 minus eight X plus seven race to the power of 1/3 is equal to zero. Now, before we start solving for X, let's just quickly recall how we can rewrite square roots as exponents. So let's assume that we have the N through of X race to the power of A. If we wanted to rewrite this as exponential value, we can rewrite it as X to the power of A over N. This is where the exponent of the insight argument is rewritten as the numerator of the exponent and the number in front of the square root gets rewritten as the denominator of the exponent. So if we use this rule on the current equation, we can rewrite the equation as the cube root of six X plus 11 minus the cube root of eight X plus seven. Now what I want to go ahead and do is add the cube root of eight X plus seven to both sides of the equation. This is going to give me the cube root of six X plus 11 is equal to the cube root of eight X plus seven. Now, what I wanna do is remove the insight arguments of both the cube roots. In order to cancel the cube roots, I wanna raise both sides of the equation to the third power. And doing this is gonna leave me with six X plus 11 is equal to eight X plus seven. Now, in order to solve for X, I'm going to subtract both sides of the equation by six X. And I'm going to subtract seven to both sides of the equation. And doing this is going to leave me with two X is equal to 11 minus seven, which is four. And finally, I'm going to divide both sides of the equation by two and this is going to give me X is equal to two and this is going to be the solution to the given equation. And with that being said, the answer to this problem is going to be B so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see well in the next video.

Solve each equation. See Example 7. (3x+7)^1/3-(4x+2)^1/3=0

Key Concepts

Cube Roots

Isolating Variables

Cubing Both Sides

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