What is an Equation  An equation is an expression with an ‘equal’ sign and another expression.  EXAMPLE:  x + 5 = 4  2x – 6 = 13  There is a Left side, an equal sign, and a right side.

Linear Equations  A Linear Equation is a polynomial of degree 1.  That means that the exponent is a one.  Example:  x = 4  2x 1 – 6 = 13

QUADRATIC EQUATIONS  A quadratic equation is a polynomial with a degree 2.  Which means that the exponent is a 2.  Example:  x 2 - 3x – 10 = 5  x = 2

Solving Equations  In order to solve for the unknown variable, you must isolate the variable using the zero effect.  ZERO EFFECT: For every positive cancels out every negative to equal zero.  Example:  (+4) = 0  17 + (-17) = 0

Solving Equations  The goal to solve an equation is to get the unknown variable by itself. That is isolate the variable.  To do this, you must think of an equation like a balance scale.  You must keep the equation balanced at all times.  Therefore, whatever mathematical operation you perform to the left side, you must perform the same operation to the right side.

EXAMPLE 1 x – 4 = 10 We can see from observation that the answer is 14, because 14 – 4 = 10 STEPS: 1.Isolate variable x – = x = 14 Added +4 to both sides to stay balanced Zero effect isolated the variable x

x – 3 = 4 x – 17 = 3 x + 5 = 8 x – = x = 7 Added +3 to both sides to cause the zero effect which isolated the variable x – = x = 20 Check: x – 17 = 3 (20) – 17 = 3 3 = 3 x = x + 5 – 5 = x = 3 Check: x + 5 = 8 (3) + 5 = 8 8 = 8

Two Step Solutions  Step 1 – Isolate variable using zero effect.  Step 2 – Make variable worth one whole.  If variable is greater than 1, you would divide by the number in front of the variable to make it worth one whole.

Solve: 2x – 4 = 10 Solution: 2x – = x = 14 2x 2 = 14 2 x = 7 Add + 4 to both sides to isolate the variable Divide by the number in front of the variable to make variable worth one whole. Remember that whatever you do to one side, do to the other

Solve: 3x – 3 = 4 Solution: 3x – = x = 7 3x 33x 3 = 7373 x = Add + 3 to both sides to isolate the variable Divide by the number in front of the variable to make variable worth one whole Remember that whatever you do to one side, do to the other

Solve: 5x – 17 = 3 Solution: 5x – = x = 20 5x 55x 5 = 20 5 x = 4 Add + 17 to both sides to isolate the variable Divide by the number in front of the variable to make variable worth one whole. Remember that whatever you do to one side, do to the other

Solve: 10y + 5 = 8 Solution: 10y = y = 3 10y 10 = 3 10 x = Subtract 5 from both sides to isolate the variable Divide by the number in front of the variable to make variable worth one whole. Remember that whatever you do to one side, do to the other 3 10

Two Step Solutions  Step 1 – Isolate variable using zero effect.  Step 2 – Make variable worth one whole.  If variable is less than 1(fraction), you would multiply by the denominator, to make the variable worth one whole.

Solve: Solution: = 12 Multiplied by the denominator to make the variable worth one whole. Remember that whatever you do to one side, do to the other x4x4 = 3 ) x4x4 ( 4 = 4(3) x4x4 ( 4 ) x = 12

Solve: Solution: = 18 Multiplied by the denominator to make the variable worth one whole. Remember that whatever you do to one side, do to the other x3x3 + 4 = 10 ) x3x3 ( 3= 3(6) x3x3 ( 3 ) x = – 4 = x3x3 Subtract 4 from both sides to isolate the variable

Solve: Solution: = 2 Multiplied by the denominator to make the variable worth one whole. Remember that whatever you do to one side, do to the other x4x4 = ) x4x4 ( 4 = x4x4 ( 4 ) x = ()

Class work  Make notes  Complete questions #1-4 on Lesson 1 worksheet