Open-Ended Questions (Technical)
1. Given the equation 5(x−1) + 3(2x + 9) − 2 = 4(3x − 1) + 2(4x + 3), solve for x
by first expanding the brackets and simplifying step by step.
2. Explain why collecting like terms is essential when solving linear equations.
Provide an example to illustrate your answer.
3. Consider the equation (4x + 1)(x + 3) − (x + 5)(x − 3) = (3x + 1)(x − 4).
Expand both sides and solve for x step by step.
Multiple-Choice Questions (MCQs)
1. What is a linear equation?
a. An equation with variables raised to any power
*b. An equation where the highest power of the variable is 1
c. An equation with exponents greater than 2
d. An equation with only constant terms
2. Solve for x: 6x + 5x − 2 + 4x − 1 = 36 + 7(x-1).
*a. x = 4
b. x = 5
c. x = 6
d. x = 7
3. Which of the following is a linear equation?
*a. 3x + 5 = 11
b. x² + 4x - 3 = 0
c. y = x³ - 2x
d. 5x² - 3x + 7 = 0
4. Solve for x: 5(x - 1) + 3(2x + 9) + 3 = 4(3x - 1) + 2(4x + 3).
a. x = -2
b. x = 0
*c. x = 3
d. x = 4
5. What is the first step in solving the equation (4x + 1)(x + 3) − (x + 5)(x − 3) =
(3x + 1)(x − 4)?
*a. Expand the brackets
b. Collect like terms
c. Divide both sides by 2
d. Subtract x from both sides
6. When solving 15x + 4 = 36 + 7x, what should be done first?
a. Add 4 to both sides
b. Multiply by 7
*c. Move all terms with x to one side
d. Divide by 2
7. Solve for x in 8x = 32.
a. x = 2
*b. x = 4
c. x = 6
d. x = 8
8. What is the role of inverse operations in solving linear equations?
a. They make equations harder to solve
*b. They help isolate the variable by using opposite operations
c. They change the equation randomly
d. They remove constants only
9. If an equation has no solution, what does it mean?
a. There are infinite values of x
*b. No value of x satisfies the equation
c. x is always 0
d. The equation is incorrect
10.What happens if both sides of a linear equation are equal after solving?
*a. The equation has infinitely many solutions
b. There is no solution
c. x = 0
d. The equation is incorrect
11.What is the simplified form of 6(2x - 3) - 5(x + 4) = -3x + 2?
a. x = 3
b. x = -2
c. x = 4
d. x = -1
12.Which of the following equations has only one solution?
a. 3x + 7 = 10
b. x² - 4x + 4 = 0
c. 2x + 5 = 2x + 5
d. x² - 1 = 0
13.If 3(x + 2) = 2(x - 1) + 5, what is the value of x?
a. x = 1
b. x = -1
c. x = 0
d. x = 2
14.In the equation 5x - 2 = 3x + 6, what should be done first?
a. Subtract 3x from both sides
b. Add 6 to both sides
c. Multiply by 5
d. Divide by 2
15.What is the final step when solving -9x = -18?
a. Divide both sides by -9
b. Subtract 9
c. Multiply by -18
d. Add 18 to both sides