Balance in Equations - Grade 12 Algebra
This worksheet focuses on balancing algebraic equations, understanding properties of equality, and solving for unknown variables at a Grade 12 level.
Includes
Standards
Topics
Balance in Equations
Name:
Date:
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Read each question carefully and solve for the unknown variable(s). Show all your work to maintain balance in the equations.
1. Solve the following equation for x: 3(2x - 5) + 4 = 7x - 12
2. Which property of equality justifies adding 5 to both sides of the equation x - 5 = 10 to get x = 15?
Commutative Property
Associative Property
Addition Property of Equality
Distributive Property
3. To solve the equation \(\frac{x}{3} + \frac{1}{2} = \frac{5}{6}\), the first step is to find the of the denominators, which is .
4. Solve the quadratic equation by factoring: \(x^2 - 5x - 14 = 0\)
5. An equation can have no solution, one solution, or infinitely many solutions.
True
False
6. Solve the following system of equations: \(2x + y = 7\) \(x - 3y = 0\)
7. Imagine a balance scale. If you have 'x + 3' on one side and '7' on the other, draw what you would do to remove '3' from both sides to keep the scale balanced. Use circles for numbers and a box for 'x'.
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