Welch's 2-Sample T-Test in R
Welch's 2-Sample T-Test allows testing if the mean of two samples differs significantly, accommodating unequal variances. Learn its assumptions, working principle, and how to perform it in R with a practical example analyzing apple and orange masses data.
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Presentation Transcript
Solving Equations with Variables on Both Sides
Lets Review: Two-Step Equations
Warm Up ? + ?? = ??
? +? ?= ??
What happens if you have a problem that has variables on both sides???? 3(2x+3)= 7x - 3 + x LIKE THIS ONE!!!!!
Steps to Solving: Step 1: Clear Parentheses- Use distributive property 3(2x+3)= 7x - 3 + x Step 2:Combine all like terms 6x + 9 = 7x - 3 + x Step 3:Move all variables to one side of the equation 6x + 9 = 8x -3 Step 4:Solve using inverse operations 12 =2x
Example: 3x 8 = 5x + 2 Follow steps: Check your solution by substituting the value back into the original equation.
Example: 6p + p + 4 = 8p + 3 Follow steps: Check your solution by substituting the value back into the original equation.
Solve. 10z 15 4z= 8 +8z-15 If variables cancel there is no solution!
Practice Solve. 1. 4x + 16 = 2x x = 8 2. 8x 3 = 15 + 5x x = 6 3. 2(3x + 11) = 6x + 4 no solution 4.x = x 9 x = 36 5. An apple has about 30 calories more than an orange. Five oranges have about as many calories as 3 apples. How many calories are in each? An orange has 45 calories. An apple has 75 calories.
Lets Summarize! What are the steps to solving with a variable on both sides? Can a problem have no solution? When?
