Math Assignment: Algebraic Equations, Variables, and Operations

This math assignment solution covers a range of fundamental algebraic concepts. It begins by explaining the operations of addition, subtraction, multiplication, and division, including how to represent these operations on a number line. The assignment then delves into solving for variables in equations, including examples of how to isolate variables and balance equations. It also explores the concept of pro-numerals and how to substitute values into equations. Furthermore, the assignment addresses word problems, translating them into algebraic expressions. The solution also includes examples of how to rewrite equations and solve for unknown variables by performing operations on both sides of the equation. The document concludes by demonstrating how to solve more complex equations involving multiple steps and operations, providing a comprehensive overview of key algebraic principles. The assignment is contributed to Desklib, a platform offering study resources.

Running head: MATH ASSIGNMENT 1
Math Assignment
Name
Institution

MATH ASSIGNMENT 2
Math Assignment
Question 2
Part a
To subtract a number is similar to add the opposite of the number. For example, if we want to
compute ( −5−9 ) =−5+(−9). Note, we change the subtraction sign to addition sign on the
second number. On the number line, we start by indicating the first number (−5) then move 9
steps to the left to get -14.
Also, in case we want to compute −4−(−7) we write the problem as an addition problem. That
is, −4− (−7 )=−4+ 7. On the number line, we start by writing -4 then move 7 steps to the right to
get 3.
Part b
For both multiplication and division, if the signs are the same (both negative or positive) the
result is always positive.
For both multiplication and division, if the signs are different (one negative and the other
positive) the result is always negative.
Question 2
Part a
Let the missing numbers be x and y in the first and second column respectively. Then, we form
the equations 20 x=1400∧20 y =−60. Solving the two equations yields,

MATH ASSIGNMENT 3
20 x=1400 , x=144
20 =70
20 y=−60 , y =−60
20 =−3
Therefore, the missing numbers are 70 and -3.
Part b
The result is ( 1400+280−60−12 ) =1608
Question 3
Part a
Pro-numerals or variables
Part b
Temperature= 5
9 ( F−32). Then, replacing the variable F with 95 and substituting yields:
Temperature= 5
9 ( 95−32 ) =35℃
Question 4
Part a
Balanced
Part b
To ‘undo’ −5a in an equation you would +5a both sides.

MATH ASSIGNMENT 4
To ‘undo’ ×7 in an equation you would ÷ 7on both sides.
To ‘undo’ ÷ 3in an equation you would ×3 on both sides.
Part c
I would add +5 to both sides to solve for x in the equation x−5=3
Part d
x−5=3
Adding +5 to both sides of the equation results to:
x−5+5=3+5
x=8
Question 5
Word/Phrase Operation
Difference -
Triple ×
Increased by +
Per ÷
Altogether +
Fewer than -
Question 6
Part a
On the left hand side of the equation
Part b

MATH ASSIGNMENT 5
Balanced
Part c
The equation x=2 y +3 can be rewritten as 2 y+ 3=x
Then, we subtract 3 from both sides to get:
2 y+3−3=x−3
2 y=x−3
Divide both sides by 2 to get y as follows:
2 y
2 = x−3
2
Therefore, y= x−3
2