Linear Equations with a negative x term

Linear Equations with a Negative x Term

Introduction

  • Linear equations are represented in the form ax + b = c. The x value in the equation is the unknown variable that needs to be determined.
  • If x exhibits a negative value or is being deducted in the equation, then one is dealing with a linear equation with a negative x term.

Elements of a Linear Equation

  • The essential parts of a linear equation consist of a variable (x), constants (-a, b, c-), and an equals symbol (=).

Solving a Linear Equation with Negative x

  1. The equation remains balanced until the same activity (addition, subtraction, multiplication, or division) is applied to either side of the equation.
  2. To solve for x, start by eliminating the constants from the side of the equation where x resides by using additive or subtractive methods.
  3. Apply multiplication or division operations, if needed, to completely isolate x.

Examples

  • For the equation -4x + 3 = 1, start by subtracting 3 from both sides to get -4x = -2. Then divide both sides by -4 to isolate x, thus x = 1/2.
  • In the case of the equation -2x - 5 = -9, add 5 to both sides to get -2x = -4. Then divide each side by -2 to find x, thus x = 2.

Conclusion

  • Understanding how to solve linear equations, specifically those with a negative x term, is a fundamental skill in algebra.
  • Practicing these equations regularly with different examples can help to enhance skills for solving them accurately and quickly. REMEMBER, follow the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (PEMDAS).
  • Mastery of these equations can also pave the way for comprehension of more complex algebraic topics like inequalities and algebraic fractions.