Solve The Linear Equations Worksheet

Algebra 2
Equations

Total questions - 6

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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 nn.\newline2n8=4n+42n - 8 = 4n + 4
Solution:
  1. Subtract n terms: First, we want to get all the nn terms on one side of the equation and the constant terms on the other side. We can do this by subtracting 2n2n from both sides of the equation.2n82n=4n+42n2n - 8 - 2n = 4n + 4 - 2nThis simplifies to:8=2n+4-8 = 2n + 4
  2. Isolate nn term: Next, we subtract 44 from both sides to isolate the term with nn on one side.\newline84=2n+44-8 - 4 = 2n + 4 - 4\newlineThis simplifies to:\newline12=2n-12 = 2n
  3. Divide to solve nn: Now, we divide both sides by 22 to solve for nn.\newline122=2n2\frac{-12}{ 2} = \frac{2n}{2}This simplifies to:\newlinen=6n = -6
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About Worksheet

Algebra 2
Equations

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.

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