Eliminate parentheses using the distributive property.
18e -48 = 5e +43
13e -48 = 43 . . . . . . . . subtract 5e from both sides
13e = 91 . . . . . . . . . . . . add 48 to both sides
e = 7 . . . . . . . . . . . . . . divide both sides by 13
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<em>Comment on equation solving</em>
If there are parentheses or fractions, it usually works well to eliminate those. The distributive property is used to eliminate parentheses. Fractions can be eliminated by multiplying the equation by the denominator. (We mean 'multiply both sides of the equation by the denominator'.) If you have excellent skill with arithmetic using fractions, you don't need to go to the trouble to eliminate them.
After the numbers in the equation are mainly integers or decimals, the next step is to look to see where the variable of interest is located. You want to do what it necessary to put all of the variable terms on one side of the equal sign, and everything else on the other side. The procedure generally is to decide what you don't want, and subtract that from both sides of the equation.
Finally, you divide by the coefficient of the variable, so the variable stands alone on one side of the equal sign. This shows you the solution.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.
140 = 110 + 2 x 15.
These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.