# Solve The Linear Equations Worksheet

## 6 problems

Solving linear equations involves finding the values of variables that make the equation true. For a single equation like $$ax + b = 0$$, you solve for $$x$$. For systems of equations with multiple variables, methods include graphing, substitution, elimination, and using matrices. These techniques help find the intersection points or common solutions and are widely used in various fields such as science, engineering, and economics.

Algebra 2
Equations

## How Will This Worksheet on "Solve the Linear Equations" Benefit Your Student's Learning?

• Build a strong foundation in algebra.
• Provide ample practice in solving linear equations.
• Enhance students' overall problem-solving abilities.
• Promote logical and analytical thinking.
• Teach the step-by-step process of isolating variables.
• Boost confidence in handling algebraic expressions.
• Reinforce understanding of algebraic concepts.
• Prepare students for more advanced mathematical studies.

## How to Solve the Linear Equations?

• Simplify both sides of the equation if necessary by combining like terms and distributing.
• Use addition or subtraction to move all variable terms to one side of the equation and all constant terms to the other side.
• Use multiplication or division to isolate the variable on one side of the equation.
• Perform the necessary operations to solve for the variable.
• Substitute your solution back into the original equation to verify it is correct.

## Solved Example

Q. Solve for $n$.$\newline$$2n - 8 = 4n + 4$
Solution:
1. Subtract n terms: First, we want to get all the $n$ terms on one side of the equation and the constant terms on the other side. We can do this by subtracting $2n$ from both sides of the equation.$2n - 8 - 2n = 4n + 4 - 2n$This simplifies to:$-8 = 2n + 4$
2. Isolate $n$ term: Next, we subtract $4$ from both sides to isolate the term with $n$ on one side.$\newline$$-8 - 4 = 2n + 4 - 4$$\newline$This simplifies to:$\newline$$-12 = 2n$
3. Divide to solve $n$: Now, we divide both sides by $2$ to solve for $n$.$\newline$$\frac{-12}{ 2} = \frac{2n}{2}$This simplifies to:$\newline$$n = -6$

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”