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Simplifying Expressions

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Simplifying Expressions

Simplifying expressions is one of the core basics for algebra simplification. The goal is taking the distributive property, which is used to apply multiplying a number by a group of numbers added together, but it is used in the removal of the parentheses. It is combining Like Terms, which must have the same variable or exponent and simplifying those expressions. We are taking these algebraic expressions and applying the five core terms in this step by step evaluation of the three given equations. The following three given expression will be shown how to actively use the distributive property in order to accurately succeed in the removal of the parentheses. 2a(a-5) + 4(a-5) The Given Expression. 2a2-10a+4(a-5) The distributive property includes the variables added to the exponent.
2a2-10a+4a-20 The distributive property removes the parentheses.
2a2-6a-20 Adding the coefficients by the combined Like Terms.
The simplified expression: 2a2-6a-20.
The expression doesn’t need to be simplified longer since nothing else can go into the expressions since the like terms have already been simplified in order. While simplifying the following expressions, the properties of real numbers will be used and identified. The math work will be aligned on above on the left while the discussion of properties is on the right side of each line.
2w-3+3(w-4)-5(w-6) The Given Expression

2w-3+3w-12-5(w-6) The distributive property includes the variable added to the exponent.

5w-15-5w-30 The distributive property removes the parentheses. 0.050.3m+35n)-0.8(-0.09n-22m) The Given Expression 0.015m+1.75n-0.8(-0.09n-22m 0.015m+1.75n-0.8(-22m-0.09n)
0.015m+1.75n+17.6m−0.072n The distributive property removes the parentheses.
17.615m+1.822n
0.015m+17.6m+1.75n-0.072n Like terms are arranged together using the commutative property. All terms are variable terms but only those with the same variable may be combined.
17.615m+1.678n Like Terns are combined by adding coefficients.

In algebraic expressions the five terms exist in order to take each expression and simplify them in like terms. I developed a certain rotation in how to simplify each expression and with wrong step in between the simplifying the problem than the answer would be deemed incorrect. I took the distributive property which ended in the removal of the parentheses. I grouped them into like terms so they could be combined with the same variable. With the commutative property allows movement of terms.
Inequalities
According to the text, Elementary and Intermediate algebra (Dugopolski, 2012), the text states, “Medical professionals say that two-thirds of all Americans are overweight and excess weight has about the same effect on life expectancy as smoking. How can you tell if you are overweight or normal? Body mass index (BMI) can help you decide. To determine BMI divide your weight in kilograms by the square of your height in meters. Don't know your weight and height in the metric system? Then use the formula BMI = 703W/H2, where W is your weight in pounds and H is your height in inches. If 23 < BMI < 25, then you are probably not overweight (Dugopolski, 2012). I’ll be formatting the different intervals in each formula and the compound inequalities that are presented in order to decipher each interval. I will be using my height of 70 inches in order to plug in the BMI formula= 703WH2.

Formula basic: 703WH2 is the basis of the entire paper and what I will be using as a reference to the four reaming problems.
17< BMI < = 22 Might have a longer life span that average.
17 < 703W < 22 H2
17 < 703W <22 This is called an equivalent inequality as the BMI is being replaced.

(70)2 H2 has been taken by the height in inches.
17<703W<22
4900 Now the denominator will be multiplied twice in each term in the numerator. 17, 703W, and 22.
17(4900) < 703W (4900) < 22 (4900) 4900
83300 < 703W<107800 All the terms are divided by 703 to carry out W. 703
118 < W<153 The solution shows the range for weight people of height of 70 inches might have a longer life span if they were between 118 and 153 pounds.
The next problem is to figure out which weight range of people is not overweight. In this formula I am applying the same method, but in turn I am taking this inequality and substituting W for the height.
23 <BMI< =25 Probably not overweight
23 <703W<25 Instead of W, I’ll multiply H2 and taking it out of the denominator.
23H2 <703W<25H2 / 703 Dive the terms by 703 to single out the W.
23H2 <W<25H2 This is an equivalent inequality. The height will be (4900) which will be
703 703 substituted into the formula to the intervals 2nd weight.
23(4900)<W<25(4900)
703 703 112700<W<122500 The intervals were multiplied.
703 703

160<W<174 The division has been set.

People who are 70 inches in height who weigh between 160 pounds and 174 pounds are probably overweight. The next interval is where I determine the obesity range for people of height of 70 inches.
25<BMI < =30 Probably overweight
25.1(4900) < W<29.9(4900) Division,
703 703

175 < W < 208
People of height of 70 inches who weight between 175 and 208 are probably overweight. The next interval deals with obesity of a certain extent. I am substituting 30 for 29.9.
W > 30 (4900)
703

W> 147000 Multiplication has taken place. 703
W> 209 Division has taken place.

W> 209 are probably obese.

People of height of 70 inches who weigh 209 pounds or above are more like to be obese or headed for that weight bracket unless serious measures are taken into action.
People of 70 inches who weigh between 160 and 174 lbs. are probably not overweight, so in order to garner height for this formula I will let X=the quantity of those who are not overweight.
X = {w l w > 160 and w <174} is for a person’s weight.
X = (160, 174)
-----------(--------------------------)-----------------------
160 174 By applying the intervals with the three compound equalities I was able to determine the weight range of each BMI (Body Mass Index) for each formula. I solved for W and H2. I used a height of 70 inches to come to each conclusion for the given formulas and solved. The formulas are no different than solving equations, the system is the same except the method has been changed with the variables becoming inequalities from a start to finish interval.

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