Solving Linear Equations

Last Updated : 14 December 2023, Thursday

Table of Topics
Solution to the Equation Meaning
Subtraction, addition, division,multiplication properties of equality
Translating an equation and solving
General strategy to solve linear equations

Solution to the Equation Meaning

  • Value of the variable that makes the equation true is called solution to the equation
  • For example, 2 is the solution to equation 5x-3=7

Subtraction, addition, division,multiplication properties of equality

Subtraction Property of Equality

For all real numbers ๐‘Ž,๐‘, and ๐‘, if ๐‘Ž=๐‘, then ๐‘Žโˆ’๐‘=๐‘โˆ’๐‘

Addition Property of Equality

For all real numbers ๐‘Ž,๐‘, and ๐‘, if ๐‘Ž=๐‘, then ๐‘Ž+๐‘=๐‘+๐‘

Division and multiplication properties of equality

properties of equalities

Translating an equation and solving

  • These words translate to Equal sign (=) :
    • is
    • is equal to
    • is the same as
    • the result is
    • gives
    • was
    • will be
  • Example : five more than x is equal to 26

General strategy to solve linear equations

Step 1. Simplify each side of the equation as much as possible. Use the Distributive Property to remove any parentheses. Combine like terms.

Step 2. Collect all the variable terms to one side of the equation. Use the Addition or Subtraction Property of Equality.

Step 3. Collect all the constant terms to the other side of the equation. Use the Addition or Subtraction Property of Equality.

Step 4. Make the coefficient of the variable term to equal to 1. Use the Multiplication or Division Property of Equality. State the solution to the equation.

Step 5. Check the solution. Substitute the solution into the original equation to make sure the result is a true statement.