LINEAR EQUATION in One Variable A linear equation

LINEAR EQUATION in One Variable

A linear equation in one variable is an equality between 2 algebraic expressions involving 1 variable where exponent is 1. What is EQUATION? What is a VARIABLE? “How to solve linear equation? ”

To solve linear equations, you add, subtract, multiply and divide both sides of the equation by numbers and variables, so that you end up with a single variable on one side and a single number on the other side. Review on PROPERTIES OF EQUALITY Examples of solving Linear Equation

EQUATION An equation is a statement that two quantities are equivalent. For example: x + 1 = 4 2 y – 15 = 38 … BACK

Example 1 x + 1 = -3 1. Subtract 1 from both sides: x + 1 - 1 = -3 - 1 2. Simplify both sides: x = -4 NEXT…

Example 2 2 x + 1 = -17 1. Subtract 1 from both sides: 2 x + 1 - 1 = -17 - 1 2. Simplify both sides: 2 x = -18 3. Divide both sides by 2: 2 x = -18 2 2 4. Simplify both sides: x = -9 NEXT…

Example 3: 5(x - 4) = 3 x + 2 1. Expand brackets: 5 x - 20 = 3 x + 2 2. Subtract 3 x from both sides: 5 x - 20 - 3 x = 3 x + 2 - 3 x 3. Simplify both sides: 2 x - 20 = 2 4. Add 20 to both sides: 2 x - 20 + 20 = 2 + 20 5. Simplify both sides: 2 x = 22 6. Divide both sides by 2: 2 x = 22 2 2 7. Simplify both sides: x = 11 NEXT…

Example 4: 2 x + 5 = 9 - 7 x 1. Transpose 7 x on the left side 2 x+5+7 x = 9 2. Transpose 5 on the right side 2 x+7 x = 9 -5 3. Simplify both sides 9 x = 4 4. Divide both side by 9 9 x = 4 9 9 5. Simplify both sides: x = 4/9 NEXT…

REVIEW: 1. Reflexive Property a = a 2. Symmetric Property If a = b, then b= a 3. Transitive Property If a = b and b = c, then a = c NEXT. .

4. Substitution If a – 6 = 4 and a = b, then b – 6 = 4 5. Addition Property of Equality (APE) If a = b, then a + c = b + c 6. Multiplication Property of Equality (MPE) If a = b, then a c = b c …BACK

VARIABLE a number that you don't know, often represented by "x" or "y" but any letter will do! Exercises on Linear Equation

Exercises: Tell whether it is an example of LINEAR EQUATION in ONE VARIABLE or Not 1. ) 5 x + 3 = 2 YES it is 2. ) -5 x + 2 y = 1 NO it isn’t 3. ) 3 xy + 2 = 6 NO it isn’t 4. ) 4 x^2 = 12 NO it isn’t 5. ) 2 x + 5 = 9 – 7 x YES it is … BACK

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