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Linear Equation In one variable class 7
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠ 0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.
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Definition of equation as a mathematical expression showing equality, along with examples.
Explanation of linear equations in one variable, given in standard forms and examples. Identifies them as first degree equations.
Defines solution and solution set; provides steps to determine if a value is a solution to an equation.
Examples showing how to check if values are solutions to specific equations with true and false comparisons.
Explains the process to solve linear equations by isolating variables using inverse operations, summarizing key steps.
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Linear Equation In one variable class 7
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- 3. Equation • Equation- amathematical expression that states that two (2) quantities are equal • ** Use the equal sign (=) ** • ex. 2 + 8 = 10 ex. 10 – 5 = 5
- 4. Type of Equation •Linear Equation in one variable- equation that can be written in the form . . . • ax + b = c or ax = b • where a, b, c are constants and a 0 • • ex. 3x + 9 = 0 ex. 7x + 5 = 2x – 9 • ex. 4(x – 2)= 6 ex. x = 6 ≠
- 5. • Linear Equation= First degree equation • ** First degree because the highest power on the variable is one. **
- 6. Solution to aLinear Equation • Solution- the value that can be substituted for the unknown variable so the resulting statement is true • Solution Set- the set of all solutions
- 7. To determine ifa value is a solution? 1. Substitute the value in for the unknown variable. 2. Simplify both sides of the equation. 3. Does it make a true statement (both sides of the equation are equal)? • If yes, then the value is a solution. • If no, then the value is not a
- 8. For example .. . ex. 4 is a solution to 3x – 5 = 7 3x – 5 = 7 3(4) – 5 = 7 12 – 5 = 7 7 = 7 True Statement ex. 2 is not a solution to 5x – 9 = 6 5x – 9 = 6 5(2) – 9 = 6 10 – 9 = 6 1 = 6 False Statement
- 9. Determine if thenumbers are solutions to the following equations. • ex. ½ ; 2y + 5 = 4 • ex. 3 ; 4x + 3 = 18 – x
- 10. How to SolveLinear Equations • Isolate the variable on one side of the equation so that the number that is the solution is on the other side. Typically variable left-hand side solution right-hand side **But it does not matter which side is which
- 11. To isolate thevariable use Inverse Operations Inverse Operations- Operations that undo each other. • Addition and Subtraction are inverse operations. • Multiplication and Division are inverse operations.
- 12. Steps To SolveLinear Equations 1. Simplify both sides of the equation as much as possible • Clear Fractions • Combine like terms • Use distributive property – 3(x + 5) 1. Move all variable terms to one side of the equation and all constant terms to the other side of the equation • Variables-left side of equation, Constants-right side of equation • Use addition or subtraction (Do opposite of what is given) 1. Isolate variable (make the coefficient 1) on one side of equation and solution on the other side • Use multiplication or division (Do opposite of what is given) 1. Check that your solution is correct by substituting it back