Linear Equations with a positive x term

Linear Equations with a Positive x Term

Introduction

  • Linear equations are of the form ax + b = c. They are called linear because the graph representing such equations is a straight line.
  • The term x in the equation is the unknown which we need to solve for. If x is positive, it means that it is being added in the equation.

Parts of a Linear Equation

  • A linear equation primarily consists of three parts: a variable (x), constants (-a, b, c-), and an equals sign (=).

Process of Solving a Linear Equation with Positive x

  1. An equation remains balanced as long as you do the same operation (add, subtract, multiply or divide) on both sides of that equals sign.
  2. To isolate x, first perform additive or subtractive operations to eliminate the constants from the side of the equation where x resides.
  3. Then, perform multiplicative or divisive operations, if necessary, to completely isolate x.

Examples

  • For an equation 3x + 4 = 10, to begin isolating x, subtract 4 from both sides of the equation, to get 3x = 6. Then divide both sides by 3 to find x, getting x = 2.
  • In the equation 7x - 3 = 11, adding 3 to both sides of the equation isolates the term with x, giving 7x = 14. Dividing both sides by 7 fully isolates x and hence, x = 2.

Conclusion

  • Solving linear equations with a positive x term is a foundational skill in algebra.
  • Regular practice with different types of linear equations can help you to quickly and correctly solve them, it’s important to remember the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (PEMDAS).
  • Being comfortable with these equations can also support understanding of inequalities, algebraic fractions, and other advanced topics.