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Worksheet: Linear Equations with Variables on Both Sides
Q3:
Given that , find .
Q4:
William believes the equation can have more than one solution for special values of and . Is he right? If so, what are the values?
- Ayes, ,
- Byes, ,
- Cno
- Dyes, ,
Q5:
Find the solution set of using the substitution set .
- A
- B
- C
- D
- E
Q6:
Solve .
- A
- BThere is an infinite number of solutions as the equation is always true.
- C
- DThere is no solution for
- E
Q7:
Find the value of in the equation .
- A
- B
- C 2
- D
- E
Q8:
Solve .
- A
- B
- C
- DThere is no solution for .
- E
Q9:
Solve .
- A
- B
- C
- D
- E
Q10:
If is isosceles, where , , , and , find the length of each side.
- A , ,
- B , ,
- C , ,
- D , ,
- E , ,
Q11:
Find the value of given the following information:
- is on the line between and .
- .
- .
- .
Q12:
Point is the midpoint of segment . Given that the length of is , and that of is , what is the length of ?
Q13:
Given that , use the information in the figure to find the perimeter of triangle .
Q14:
Mason and Jacob are going on vacation together. Mason has $400 and Jacob has $350. Given that, on average, Mason spends $28 and Jacob spends $26 per day, after how many days will they have the same amount of money left?
- A 13 days
- B 50 days
- C 30 days
- D 25 days
- E 15 days
Q15:
Determine the value of that makes the equation true for all values of .
Q16:
80 students decided to buy a present for their teacher. They split into two groups of 40 and each student in the first group gave . In the second group, three-fifths of the students gave dollars each, and the rest contributed a total of $288. Given that the two groups contributed the same amount, find the value of .
- A36
- B16
- C20
- D12
- E26
Q17:
The equation can be solved in three steps. Which of the following is NOT a valid first step of such a method?
- A Take away from both sides.
- B Take away from both sides.
- C Take away 5 from both sides.
- D Divide both sides by 5.
- E Take away 10 from both sides.
Q18:
Solve .
- A
- B
- C
- D
- E
Q19:
Determine the solution set of the equation using the substitution set .
- A
- B
- C
- D
Q20:
Solve .
- A
- BThere is no solution for .
- C
- DThere is an infinite number of solutions as the equation is always true.
- E
Q21:
What is the value of if the equation has no solutions?