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# Evaluate the algebraic expressions below (no decimal answers)

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Evaluate the algebraic expressions below (no decimal answers)

1. N^2 - 25      a) when n=-10      b) when n=-5    c) when n=1/2    d) when n=9

2. (-7d + 14)/2      a) when d=2    b) when d=-2      c) when d= 6/7    d)  when d=4

3. 2x^-2 - x          a) when x=2      b) when x=-1    c)  when x= 1/4

Guest Jul 1, 2017

#1
+1214
+2

Evaluating these algebraid expressions just requires you to substitute in the values given for the variable. Let's do the first one together:

1. $$N^2-25$$

a) When n=-10

 $$N^2-25$$ Replace N, the variable, with -10 and evaluate from there. $$(-10)^2-25$$ Do $$(-10)^2=-10*-10=100$$ first so to adhere to the order of operations. $$100-25$$ $$75$$

The process repeats for the other values for N

b) n=-5

 $$N^2-25$$ $$(-5)^2-25$$ $$25-25$$ $$0$$

c) n=1/2

 $$N^2-25$$ $$(\frac{1}{2})^2-25$$ Remember that squaring a fraction follows the rule that $$(\frac{a}{b})^2=\frac{a^2}{b^2}$$ $$\frac{1^2}{2^2}-25$$ Simplify the fraction. $$\frac{1}{4}-25$$ Change 25 to an improper fraction so that you can subtract it from 1/4. $$\frac{25}{1}*\frac{4}{4}=\frac{100}{4}$$ Now that we have changed 25 to a fraction with a common denominator, reinsert it back into the equation. $$\frac{1}{4}-\frac{100}{4}$$ Subtract the fractions. $$-\frac{99}{4}=-24\frac{3}{4}$$ The fraction is already in simplest form. I've provided both versions of the answer.

d) n=9

 $$N^2-25$$ $$9^2-25$$ $$81-25$$ $$56$$

I'll do half of the next one and the rest are up to you to complete:

2. $$\frac{-7d+14}{2}$$

a) d=2

 $$\frac{-7d+14}{2}$$ Substitute the given value for d, 2. $$\frac{-7*2+14}{2}$$ Do -7*2 first. $$\frac{-14+14}{2}$$ Simplify the numerator by calculating -14+14. $$\frac{0}{2}=0$$

b) d=-2

 $$\frac{-7d+14}{2}$$ $$\frac{-7*-2+14}{2}$$ A negative times a negative always results in a positive. $$\frac{14+14}{2}$$ $$\frac{28}{2}$$ Divide 28 by 2. $$14$$
TheXSquaredFactor  Jul 2, 2017
Sort:

#1
+1214
+2

Evaluating these algebraid expressions just requires you to substitute in the values given for the variable. Let's do the first one together:

1. $$N^2-25$$

a) When n=-10

 $$N^2-25$$ Replace N, the variable, with -10 and evaluate from there. $$(-10)^2-25$$ Do $$(-10)^2=-10*-10=100$$ first so to adhere to the order of operations. $$100-25$$ $$75$$

The process repeats for the other values for N

b) n=-5

 $$N^2-25$$ $$(-5)^2-25$$ $$25-25$$ $$0$$

c) n=1/2

 $$N^2-25$$ $$(\frac{1}{2})^2-25$$ Remember that squaring a fraction follows the rule that $$(\frac{a}{b})^2=\frac{a^2}{b^2}$$ $$\frac{1^2}{2^2}-25$$ Simplify the fraction. $$\frac{1}{4}-25$$ Change 25 to an improper fraction so that you can subtract it from 1/4. $$\frac{25}{1}*\frac{4}{4}=\frac{100}{4}$$ Now that we have changed 25 to a fraction with a common denominator, reinsert it back into the equation. $$\frac{1}{4}-\frac{100}{4}$$ Subtract the fractions. $$-\frac{99}{4}=-24\frac{3}{4}$$ The fraction is already in simplest form. I've provided both versions of the answer.

d) n=9

 $$N^2-25$$ $$9^2-25$$ $$81-25$$ $$56$$

I'll do half of the next one and the rest are up to you to complete:

2. $$\frac{-7d+14}{2}$$

a) d=2

 $$\frac{-7d+14}{2}$$ Substitute the given value for d, 2. $$\frac{-7*2+14}{2}$$ Do -7*2 first. $$\frac{-14+14}{2}$$ Simplify the numerator by calculating -14+14. $$\frac{0}{2}=0$$

b) d=-2

 $$\frac{-7d+14}{2}$$ $$\frac{-7*-2+14}{2}$$ A negative times a negative always results in a positive. $$\frac{14+14}{2}$$ $$\frac{28}{2}$$ Divide 28 by 2. $$14$$
TheXSquaredFactor  Jul 2, 2017

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