1-Step & 2-Step Linear Equations: Balance Scale & Inverse Operations
Solving linear equations is the foundational skill of algebra. The Golden Rule of Algebra states that whatever operation you perform on one side of the equals sign, you must perform on the other side to keep the balance scale in perfect equilibrium.
๐ง Core Mental Strategies & Shortcuts
โ๏ธ Inverse Operation Pairing
Addition undoes subtraction (and vice versa). Multiplication undoes division (and vice versa): to solve 7x = 56, divide both sides by 7 (x = 8).
โก 2-Step Equation Hierarchy ("Reverse PEMDAS")
When solving ax + b = c, undo addition/subtraction first (ax = c โ b), then undo multiplication/division last (x = (c โ b) / a).
๐ฏ Negative Signs Division Rule
Dividing by a negative flips the sign: โ4x = 28 โ x = 28 รท (โ4) = โ7.
โ Frequently Asked Questions
What is the fastest way to solve a 1-step linear equation?
Identify what is happening to the variable x, and perform the exact opposite operation to both sides of the equals sign.
How do you check if your linear equation solution is correct?
Substitute your calculated answer back in place of x in the original equation. If the left side equals the right side, your answer is 100% correct.
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