# solve the equation, give steps!

Use your knowledge of:

1. fractional exponents

2. negative exponents

Solve the following equation for x

0 = (1.5)x^0.5 - (0.5)x^-0.5

### Comments for solve the equation, give steps!

 Mar 12, 2011 Solve the Equation by: Staff The question: 0 = (1.5)x^0.5 - (0.5)x^-0.5 The answer: Before we start solving the equation, I’d like to review a couple of things: First, x^0.5 is stands for x raised to the ½ power. x^0.5 means the square root of x. Second, x^-0.5 is a negative exponent: x raised to the minus ½ power. x^-0.5 means 1 divided by the square root of x x^-0.5 = 1/(x^+0.5) Including the + sign is not necessary. I’ve included the + sign to make a point. This would normally be written as follows: x^-0.5 = 1/(x^0.5) Back to the equation: 0 = (1.5)x^0.5 - (0.5)x^-0.5 0 = (1.5)sqrt(x) - (0.5)/sqrt(x) Multiply each side of the equation by sqrt(x) 0 * sqrt(x) = [(1.5)sqrt(x) - (0.5)/sqrt(x)] * sqrt(x) 0 = [(1.5)sqrt(x) - (0.5)/sqrt(x)] * sqrt(x) Using the distributive law 0 = (1.5) * sqrt(x) * sqrt(x) – [(0.5)/sqrt(x)] * sqrt(x) The sqrt(x) multiplied by the sqrt(x) = x 0 = (1.5) * x – [(0.5)/sqrt(x)] * sqrt(x) 0 = (1.5) * x – 0.5 * [sqrt(x)/sqrt(x)] The sqrt(x) divided by the sqrt(x) = 1 0 = (1.5) * x – 0.5 * 1 0 = (1.5) * x – 0.5 Add 0.5 to each side of the equation 0 + 0.5 = (1.5) * x – 0.5 + 0.5 0.5 = (1.5) * x – 0.5 + 0.5 0.5 = (1.5) * x + 0 0.5 = (1.5) * x Divide each side of the equation by 1.5 0.5/1.5 = (1.5) * x/1.5 1/3 = (1.5) * x/1.5 1/3 = (1.5/1.5) * x 1/3 = 1 * x 1/3 = x The final answer is: x = 1/3 It’s a good idea to check the work. You can check this work by substituting 1/3 for x in the original equation and using a calculator. 0 = (1.5)x^0.5 - (0.5)x^-0.5 0 = (1.5)*(1/3)^0.5 - (0.5)*(1/3)^-0.5 0 = 0.866025 - 0.866025 0 = 0 Since 0 does = 0, the solution of x = 1/3 is correct. Thanks for writing. Staff www.solving-math-problems.com

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