Linear Equation In one variable class 7

This is a slide show on linear equation in one variable for class 7 students

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3. Equation
•Equation- a mathematical 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
¹

5. •Linear Equation = First degree
equation
•** First degree because the highest
power on the variable is one. **

6. Solution to a Linear
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
• Used to show solution set { }

7. To determine if a 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
solution.

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 the numbers are
solutions to the following
equations.
•ex. ½ ; 2y + 5 = 4 •ex. 3 ; 4x + 3 = 18
– x

10. How to Solve Linear
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 the variable 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 Solve Linear
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
into original equation to see if it makes a true statement
(both sides equal the same value)