Balancing Equations: Grade 11 Algebra
This worksheet focuses on understanding and applying the concept of balance in algebraic equations for Grade 11 students, including multi-step equations and real-world problems.
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Balancing Equations: Grade 11 Algebra
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Read each question carefully and show all your work. Remember to maintain balance on both sides of the equation.
1. Explain in your own words what it means for an equation to be "balanced". You may use the image below to help illustrate your point.
2. Complete the following statements about maintaining balance in equations:
a) If you add a number to one side of an equation, you must the same number to the other side.
b) If you multiply one side of an equation by a number, you must the other side by the same number.
c) The property of equality states that if a = b, then b = a.
d) The property of equality states that if a = b and b = c, then a = c.
3. Solve the following equations, showing each step and how you maintain balance:
a) 3x - 7 = 14
b) (2/3)y + 5 = 11
c) 4(z + 2) - 5 = 15
4. Which of the following equations is NOT balanced?
5x + 2 = 2x + 8
3(x - 1) = 3x - 3
x^2 + 4 = (x + 2)^2
7 - (x + 1) = 6 - x
5. Sarah is buying apples and oranges. Apples cost $1.50 each and oranges cost $0.75 each. She buys twice as many apples as oranges and spends a total of $10.50. Write an equation to represent this situation and solve it to find out how many apples and oranges she bought.