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.

Grade 12 Math AlgebraBalance in Equations

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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSA.REI.A.1CCSS.MATH.CONTENT.HSA.REI.B.3CCSS.MATH.CONTENT.HSA.CED.A.1

Topics

AlgebraEquationsBalanceGrade 12Math

9 sections · Free to use · Printable

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Balance in Equations

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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'.