Question

name:
8.3.1 order of operations
please excuse my dear aunt sally.
p = parentheses
e = exponentiation
m = multiplication
d = division
a = addition
s = subtraction
8.3.2 negative paranoia
if x = -2, what is -3(x)² + 4 ?

1. if x = 6, what is the value of 2x² - 11x ?

a. -138
b. -6
c. 6
d. 138

1. what is the value of the expression x(x + 3)², if x = 2 ?

f. 20
g. 25
h. 27
j. 50

1. if x = -5, what is the value of \\(\frac{x² + 1}{x² - 1}\\) ?

a. \\(-\frac{9}{11}\\)
b. \\(\frac{9}{11}\\)
c. \\(\frac{12}{13}\\)
d. \\(\frac{13}{12}\\)

Explanation:

Step1: Substitute x=6 into expression

$2(6)^2 - 11(6)$

Step2: Calculate exponents first

$2(36) - 11(6)$

Step3: Perform multiplication

$72 - 66$

Step4: Perform subtraction

$72 - 66 = 6$

Step1: Substitute x=2 into expression

$2(2 + 3)^2$

Step2: Simplify parentheses first

$2(5)^2$

Step3: Calculate exponents

$2(25)$

Step4: Perform multiplication

$2 \times 25 = 50$

Step1: Substitute x=-5 into expression

$\frac{(-5)^2 + 1}{(-5)^2 - 1}$

Step2: Calculate exponents

$\frac{25 + 1}{25 - 1}$

Step3: Simplify numerator and denominator

$\frac{26}{24}$

Step4: Reduce the fraction

$\frac{26 \div 2}{24 \div 2} = \frac{13}{12}$

Answer:

1. C. 6
2. J. 50
3. D. $\frac{13}{12}$