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In this lesson, we will learn how to solve equations in which the variable is on each side of the equation.

Q1:

π π π π is a rectangle where π π = 9 π₯ β 8 and π π = 8 π₯ + 1 . Find π π .

Q2:

Find the value of π₯ .

Q3:

Given that 6 π₯ + π + 8 = 6 π₯ β 2 , find π .

Q4:

Nabil believes the equation can have more than one solution for special values of and . Is he right? If so, what are the values?

Q5:

Find the solution set of 8 π₯ 3 = π₯ + 5 using the substitution set { 2 4 , 1 1 , 3 , 7 } .

Q6:

Solve 3 ( 4 π₯ β 1 2 ) + 8 = 1 2 π₯ β 6 .

Q7:

Find the value of π in the equation π οΌ 1 8 + 1 2 ο = π Γ 1 8 + β 1 6 Γ 1 2 .

Q8:

Solve π₯ + 3 ( 2 π₯ + 4 ) = 7 π₯ + 4 .

Q9:

Solve 8 β 2 οΌ 3 π₯ 2 + 4 ο = β 5 π₯ + 2 .

Q10:

If β³ π½ πΎ πΏ is isosceles, where π½ πΎ β πΎ πΏ , π½ πΎ = 3 π₯ + 3 , πΎ πΏ = 5 π₯ β 3 , and πΏ π½ = 4 π₯ + 2 , find the length of each side.

Q11:

Find the value of π΅ πΆ given the following information:

Q12:

Point π is the midpoint of segment π π . Given that the length of π π is 2 π₯ β 1 8 , and that of π π is 3 0 β 2 π₯ , what is the length of π π ?

Q13:

Given that π β π΅ = π β πΆ , use the information in the figure to find the perimeter of triangle π΄ π΅ πΆ .

Q14:

Nader and Bassem are going on holiday together. Nader has $400 and Bassem has $350. Given that, on average, Nader spends $28 and Bassem spends $26 per day, after how many days will they have the same amount of money left?

Q15:

Determine the value of π¦ that makes the equation 6 ( π₯ + 8 ) + 9 π₯ = π¦ π₯ + 4 8 true for all values of π₯ .

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 $ π₯ . In the second group, three-fifths of the students gave 2 3 π₯ dollars each, and the rest contributed a total of $288. Given that the two groups contributed the same amount, find the value of π₯ .

Q17:

The equation 2 π₯ + 1 0 = 5 π₯ + 5 can be solved in three steps. Which of the following is NOT a valid first step of such a method?

Q18:

Solve 5 π₯ + 1 2 = 2 π₯ β 6 .

Q19:

Determine the solution set of the equation 3 ( π₯ β 1 ) = π₯ + 9 using the substitution set { 1 5 , 1 2 , 6 , 5 } .

Q20:

Solve 4 π₯ + 3 2 ( 2 0 β 8 π₯ ) = β 2 π₯ β 3 ( β 1 0 + 2 π₯ ) .

Q21:

What is the value of π if the equation 1 2 π₯ = π ( π₯ + 3 ) has no solutions?

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