Write & Solve Linear Equations Worksheets

Printable “Algebra” worksheets:
Write Equations Using Symbols
Write Linear & Nonlinear Expressions
Write & Solve Linear Equations
Solve Linear Equations (Distributive)
Solve Linear Equations in Disguise
Solve Linear Equations Word Problems

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 learn how to use of the properties of equality to solve linear equations having rational coefficients.

How to use of the properties of equality to solve linear equations?

Solving linear equations with rational coefficients using the properties of equality, involves isolating the variable on one side of the equation.

Here are the steps:

1. Understand the Properties of Equality
   The properties of equality allow you to perform the same operation on both sides of an equation without changing the equation’s solution. The key properties are:
   Addition Property of Equality: If a = b, then a+c = b+c.
   Subtraction Property of Equality: If a = b, then a−c = b−c.
   Multiplication Property of Equality: If a = b, then ac = bc.
   Division Property of Equality: If a = b and c ≠ 0 then a/c = b/c

2. Solving Linear Equations with Rational Coefficients
   Step 1: Eliminate Fractions (Optional but Helpful)
   You can start by eliminating fractions by multiplying both sides of the equation by the least common denominator (LCD) of all the fractions involved. This step is not mandatory, but it simplifies the equation.
   Step 2: Isolate the Variable
   Use the addition or subtraction property of equality to move all terms containing the variable to one side of the equation and constants to the other side.
   Step 3: Solve for the Variable
   Use the multiplication or division property of equality to isolate the variable.
   Step 4: Check Your Solution
   Substitute the solution back into the original equation to ensure it satisfies the equation.
   

Key Tips:

• Keep Equations Balanced: Whatever you do to one side of the equation, you must do to the other side.
• Simplify Fractions: Simplify fractions whenever possible to make calculations easier.
• Check the Solution: Always substitute your solution back into the original equation to verify that it works.

Have a look at this video if you need to review how to solve linear equations.

• Solve linear equations with fraction coefficients

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