Solving Two-Step Equations
Solving two-step equations in Grade 8 Saxon Math Course 3 requires students to apply two inverse operations to isolate the variable and find the solution. Students undo addition or subtraction first, then undo multiplication or division, checking the solution by substituting back into the original equation. Two-step equations are the bridge between one-step equations and multi-step algebraic problem solving.
Key Concepts
Property To solve a two step equation, isolate the variable by reversing the order of operations. Undo addition or subtraction first, and then undo multiplication or division.
Examples To solve $3x + 1.20 = 5.40$, first subtract $1.20$ to get $3x = 4.20$, then divide by $3$ to find $x = 1.4$. To solve $ 2x 5 = 9$, first add $5$ to get $ 2x = 14$, then divide by $ 2$ to find $x = 7$. To solve $\frac{x}{5} + 4 = 13$, first subtract $4$ to get $\frac{x}{5} = 9$, then multiply by $5$ to find $x = 45$.
Explanation Think of it as unwrapping a gift! You have to take off the ribbon (addition/subtraction) before you can open the box (multiplication/division). We're working backward to find the variable hiding inside. It's detective work for numbers!
Common Questions
How do you solve a two-step equation?
First, undo addition or subtraction by applying the inverse operation to both sides. Then undo multiplication or division. Check by substituting the solution back into the original equation.
What order do you use inverse operations in a two-step equation?
Undo addition and subtraction first (these are farthest from the variable), then undo multiplication or division (these are closest to the variable). This is the reverse of order of operations.
How do you solve 2x + 3 = 11?
Subtract 3 from both sides: 2x = 8. Then divide both sides by 2: x = 4. Check: 2(4) + 3 = 11. Correct.
How do you check the solution of a two-step equation?
Substitute the solution back into the original equation and verify both sides are equal. If they are, the solution is correct.
How are two-step equations used in Saxon Math Course 3?
Saxon Math Course 3 uses two-step equations throughout word problems involving money, ages, rates, and geometric measurements where two operations are needed to find the unknown.