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