Steps for Solving Linear Equations
This Grade 6 algebra skill from Yoshiwara Elementary Algebra outlines the step-by-step process for solving linear equations. Students learn a systematic approach: simplify both sides, use inverse operations to collect variable terms on one side and constant terms on the other, and then divide to find the solution.
Key Concepts
Property 1. Combine like terms on each side of the equation. 2. By adding or subtracting the same quantity on both sides of the equation, get all the variable terms on one side and all the constant terms on the other. 3. Divide both sides by the coefficient of the variable to obtain an equation of the form $x = a$.
Examples To solve $8x 3x + 1 = 16$, first combine like terms: $5x + 1 = 16$. Then isolate $x$: $5x = 15$, so $x = 3$. To solve $7y 5 = 3y + 11$, first gather variable terms on one side: $4y 5 = 11$. Then gather constants: $4y = 16$. Finally, divide: $y = 4$. To solve $10z (4z 5) = 23$, first remove parentheses: $10z 4z + 5 = 23$. Combine like terms: $6z + 5 = 23$. Isolate $z$: $6z = 18$, so $z=3$.
Explanation First, simplify by cleaning up each side of the equation. Next, gather all your variable terms on one side and your numbers on the other. Finally, perform the last division to find the variable's value.
Common Questions
What are the steps for solving a linear equation?
1) Simplify both sides. 2) Move variable terms to one side using inverse operations. 3) Move constants to the other side. 4) Divide both sides by the coefficient of the variable.
Why do you apply the same operation to both sides of an equation?
Applying the same operation to both sides keeps the equation balanced—both sides remain equal throughout the solving process.
What does it mean to check a solution to an equation?
Substitute the solution back into the original equation and verify that both sides are equal. This confirms the answer is correct.
What is an example of solving a linear equation?
Solve 3x - 4 = 11: add 4 to both sides (3x = 15), then divide by 3 (x = 5). Check: 3(5) - 4 = 11. Correct.
Where are steps for solving linear equations taught?
Steps for solving linear equations are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.