Simplify the following expressions Assignment

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Week 5 Problems

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1. Simplify the following expressions.
a. 52 + 8 – (9- 1) ÷ 4
ANS: 52 + 8 – (9- 1) ÷ 4
= 52 + 8 – 8 ÷ 4 (parenthesis)
= 25 + 8 – 8 ÷ 4 (exponent)
= 25 + 8 – 2 (division)
= 33 – 2 (addition)
= 31 (subtraction) (Lee, Licwinko, & Taylor-Buckner, 2013)
b.
ANS:
=
c.
ANS: =
d. [4(x -2) + 11] – [3(3x – 4) -5]
ANS: [4(x -2) + 11] – [3(3x – 4) -5]
= [4x -8 + 11] – [9x – 12 -5]
= [4x + 3] – [9x – 17]
= 4x + 3 – 9x + 17
= 4x – 9x + 3 + 17
= -5x + 20

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e.
ANS:
= (parenthesis)
= (exponent)
= (multiplication)
= (subtraction)
= 95 (modulus)
2. Evaluate:
a. -(-x) when x = 8
ANS: -(-x) = - (-8) = +8 = 8
b. -x when x = - 43
ANS: -x = - (-43) = + 43 = 43
3. Solve and graph on a number line:
a. 5x + 2(x – 3) + 2x = 6x + 3(x +2) - 4 + x
ANS: 5x + 2(x – 3) + 2x = 6x + 3(x +2) - 4 + x
=> 5x + 2x – 6 + 2x = 6x + 3x +6 - 4 + x
=> 5x + 2x + 2x – 6 = 6x + 3x + x +6 – 4
=> (5 + 2 + 2) x – 6 = (6 + 3 +1) x + 6 - 4
=> 9x – 6 = 10x + 6 – 4
=> 9x – 6 =10x + 2
=> 10x – 9x = - 6 – 2
=> x = - 8 (Earnest, 2015)
x = -8 0
b. 5x + 2 > 1 + 7x

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ANS: 5x + 2 > 1 + 7x
=> 2 – 1 > 7x - 5x
=> 1 > 2x
=> 1/ 2 > x
x = 1/2 0
c. -2 < x < 7- 3
ANS: -2 < x < 7- 3 = -2 < x < 4
x = -2 0 x = 4
4. Solve (do not graph):
a. 0.3 x + 0.9 = 0.7x – 0.6
ANS: 0.3 x + 0.9 = 0.7x – 0.6
 0.9 – 0.6 = 0.7x – 0.3 x
 0.3 = (0.7 – 0.3) x
 0.3 = 0.4 x
 0.4 x = 0.3
 x = 0.3 / 0.4 = 3 / 4 = 0.75
 x = 0.75
b. 5(2 – 4t) + 3t = -5t + 7

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ANS: 5(2 – 4t) + 3t = -5t + 7
=> 10 – 20t + 3t = -5t + 7
=> 10 – 17t = -5t + 7
=> 10 – 7 = -5t + 17t
=> 3 = 12t
=> 12t = 3
=> t = 3 / 12 = 1 / 4 = 0.25
=> t = 0.25
c. 2(2y + 3) + 7 – 3y = 2[-4y + 3(y + 3)]
ANS: 2(2y + 3) + 7 – 3y = 2[-4y + 3(y + 3)]
=> 2(2y + 3) + 7 – 3y = 2[-4y + 3y + 9]
=> 2(2y + 3) + 7 – 3y = -8y + 6y + 18
=> 4y + 6 + 7 – 3y = -8y + 6y + 18
=> 4y -3y +6 + 7 = -2y +18
=> y +13 = -2y +18
=> y + 2y = 18 – 13
=> 3y = 5
=> y = 5 / 3 = 1.67
=> y = 1.67
d.

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ANS:
=>
=>
=>
=>
=>
=>
=> 7t = 6
=>
ANS:
5. Solve for k:
ANS:
=>
=>
=>
=>
6. Solve the following problems:
a. The perimeter of a rectangular yard is 92ft. The length is 6 ft greater than
the width. Find the length and width.

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ANS: Let the width = x ft, and hence the length = (6 + x) ft
Now, area of the rectangle = width * length = x * (6 + x) = 6x + x2
According to the problem, 6x + x2 = 92
So, x2 + 6x – 92 = 0
=>
So, width = 7.05 ft, and length = (7.05 + 6) = 13.05 ft
b. The formula to change oF to oC is:
If the temperature is 14.3 oC what is it in oF?
ANS: Temperature = 14.3o C
We know
Hence,
So, temperature is 57.74o F
c. 620 is what percent of 1230?
ANS: 620 is equivalent to fraction of 1230
Hence, 620 is of 1230
Extra credit: Solve the following for r:

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ANS:
 (taking LCM)
 (taking inverse)
So,
References
Earnest, D. (2015). From number lines to graphs in the coordinate plane: Investigating problem
solving across mathematical representations. Cognition and Instruction, 33(1), 46-87.
Lee, J. K., Licwinko, S., & Taylor-Buckner, N. (2013). Exploring mathematical reasoning of the
order of operations: Rearranging the procedural component PEMDAS. Journal of
Mathematics Education at Teachers College, 4(2)