Solving Equations with Variables on Both Sides
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 1: Equations) learn the five-step strategy for solving equations with variables on both sides: simplify, collect variable terms on one side, collect constants on the other, isolate the variable, and check by substitution.
Key Concepts
Step 1. Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms. Step 2. Collect all the variable terms on one side of the equation. Use the Addition or Subtraction Property of Equality. Step 3. Collect all the constant terms on the other side of the equation. Use the Addition or Subtraction Property of Equality. Step 4. Make the coefficient of the variable term to equal to 1. Use the Multiplication or Division Property of Equality. State the solution to the equation. Step 5. Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.
Common Questions
How do you solve equations with variables on both sides in 7th grade?
Move all variable terms to one side and all constants to the other side, then divide to isolate the variable. Example: 2x + 7 = 5x - 8 gives x = 5 after subtracting 2x and adding 8 on both sides, then dividing by 3.
What is the five-step strategy for solving equations with variables on both sides?
(1) Use distributive property to remove parentheses. (2) Combine like terms. (3) Move variable terms to one side. (4) Move constants to the other side. (5) Divide to get variable alone, then check.
How do you solve 3(4x - 6) = 2(5 - x)?
Distribute: 12x - 18 = 10 - 2x. Add 2x: 14x - 18 = 10. Add 18: 14x = 28. Divide by 14: x = 2.
What chapter in Big Ideas Math Advanced 2 covers equations with variables on both sides?
Chapter 1: Equations in Big Ideas Math Advanced 2 (Grade 7) covers solving equations with variables on both sides.
How do you check your solution to an equation?
Substitute the solution back into the original equation. If both sides give equal values, the solution is correct.