1st Degree Equations
Section 2.1
1st Degree Equations
Slide: 1
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
y = 2x
The terms on both sides of the equality signs have the same value expressed in different ways.
y
Slide: 2
2x
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
× 2
If you multiply one side by something, you must do the same to the other, to keep the equation balanced.
2y
Slide: 3
y = 2x 2y = 4 x
× 2
4x 2x
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
× 2
If you multiply one side by something, you must do the same to the other, to keep the equation balanced.
2y
Slide: 4
y = 2x 2y = 4 x
× 2
4x
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
2 y + 5 = 4x + 5 If you add an amount to one side, you must also add the same amount to the other side.
2y+ 5
Slide: 5
4x + 5
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
≠ 4x + 4 2y + 5 = If the same operations are not performed on both sides, the expressions will no longer be equal.
4x + 4 2 y+ 5
Slide: 6
Equivalent Equations Equations with the same solutions are called equivalent equations.
6x +4 = 10 6x = 6 x=1
Subtract 4 from both sides.
Divide by 6 on both sides.
Slide: 7
The three equations are equivalent because x = 1 satisfies each equation.
Principle of Equations Performing the same operation on both sides of an equation will result in an equivalent equation.
We have used this rule already. To summarize: Addition principle
a+c=b+c
Adding the same amount to both sides.
Subtraction principle
a−c=b−c
Subtracting the same amount from both sides.
Multiplication principle
a × c = b× c
Multiplying the same amount to both sides.
Division principle
a ÷ c = b÷ c
Dividing by the same amount on both sides.
Slide: 8
Principle of Equations Performing the same operation on both sides of an equation will result in an equivalent equation.
We have used this rule already. To summarize: Addition principle
a+c=b+c
Adding the same amount to both sides.
Subtraction principle
a−c=b−c
Subtracting the same amount from both sides.
Multiplication principle
a × c = b× c
Multiplying the same amount to both sides.
Division principle
a ÷ c = b÷ c
Dividing by the same amount on both sides.
Slide: 9
Solve for x in the equation 5 x = 10 . 2
a. b. c. d.
Slide: 10
1.6 2.4 4 25
Solve for x in the equation 5 x = 10 . 2
Slide: 11
Solve for x in the equation 8(x + 4) = 28 − 2(x − 5).
3 5 b. 5 3 c. − 7 5 a.
d. 1 Slide: 12
Solve for x in the equation 8(x + 4) = 28 − 2(x − 5).
Slide: 13
1st Degree Equations
Slide: 1
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
y = 2x
The terms on both sides of the equality signs have the same value expressed in different ways.
y
Slide: 2
2x
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
× 2
If you multiply one side by something, you must do the same to the other, to keep the equation balanced.
2y
Slide: 3
y = 2x 2y = 4 x
× 2
4x 2x
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
× 2
If you multiply one side by something, you must do the same to the other, to keep the equation balanced.
2y
Slide: 4
y = 2x 2y = 4 x
× 2
4x
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
2 y + 5 = 4x + 5 If you add an amount to one side, you must also add the same amount to the other side.
2y+ 5
Slide: 5
4x + 5
1st Degree Equations An algebraic equation is a mathematical statement that shows the equality between two algebraic expressions or between a number and an algebraic expression.
≠ 4x + 4 2y + 5 = If the same operations are not performed on both sides, the expressions will no longer be equal.
4x + 4 2 y+ 5
Slide: 6
Equivalent Equations Equations with the same solutions are called equivalent equations.
6x +4 = 10 6x = 6 x=1
Subtract 4 from both sides.
Divide by 6 on both sides.
Slide: 7
The three equations are equivalent because x = 1 satisfies each equation.
Principle of Equations Performing the same operation on both sides of an equation will result in an equivalent equation.
We have used this rule already. To summarize: Addition principle
a+c=b+c
Adding the same amount to both sides.
Subtraction principle
a−c=b−c
Subtracting the same amount from both sides.
Multiplication principle
a × c = b× c
Multiplying the same amount to both sides.
Division principle
a ÷ c = b÷ c
Dividing by the same amount on both sides.
Slide: 8
Principle of Equations Performing the same operation on both sides of an equation will result in an equivalent equation.
We have used this rule already. To summarize: Addition principle
a+c=b+c
Adding the same amount to both sides.
Subtraction principle
a−c=b−c
Subtracting the same amount from both sides.
Multiplication principle
a × c = b× c
Multiplying the same amount to both sides.
Division principle
a ÷ c = b÷ c
Dividing by the same amount on both sides.
Slide: 9
Solve for x in the equation 5 x = 10 . 2
a. b. c. d.
Slide: 10
1.6 2.4 4 25
Solve for x in the equation 5 x = 10 . 2
Slide: 11
Solve for x in the equation 8(x + 4) = 28 − 2(x − 5).
3 5 b. 5 3 c. − 7 5 a.
d. 1 Slide: 12
Solve for x in the equation 8(x + 4) = 28 − 2(x − 5).
Slide: 13
