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Week 3

Week 3. GE127. Graph the point (-4,6). The point (-4,6) is graphed the following way: We know that x is -4 so we find -4 on our graph:. Then, we know the corresponding y is 6, so we go up 6:. Identify the X and Y intercepts.

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Week 3

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  1. Week 3 GE127

  2. Graph the point (-4,6)

  3. The point (-4,6) is graphed the following way: We know that x is -4 so we find -4 on our graph: Then, we know the corresponding y is 6, so we go up 6:

  4. Identify the X and Y intercepts

  5. The x intercept is where the line crosses the x axis.The y intercept is where the line crosses the y axis. X intercept is (2,0) Y intercept is (0,-4)

  6. Identify the X and Y intercepts

  7. The x intercept is where the line crosses the x axis.The y intercept is where the line crosses the y axis. X intercept: (-3,0) Y intercept: (0,6) X intercept: (2,0)

  8. Graph the line

  9. We know that our equation is in y=mx+b form (slope intercept form) m=slope and b=y intercept. So our slope is 3 and our y intercept is 3. We always start graphing by graphing the y-intercept first. Then we use the slope as and see that it is so we rise 3 units and run 1 unit and then draw a line through the two points.

  10. Solve the problem: 55% of what number is 44?

  11. First we review what specific words translate to equations: 55% of what number is 44? We change this to decimal .55 This is our unknown (x) OF is always multiplication IS usually translates to = So the phrase translates to the following equation: We need to get x alone so we see .55 is multiplying.. We need to divide it on both sides to get x alone. Whenever working with percents: always ask yourself if it makes sense. Does it make sense that 55% of 80 would be 44? Yes. That makes sense!

  12. Solve: When a number is decreased by 20% the result is 48.

  13. When a number is decreased by 20% the result is 48. We start this problem the same as we did the last one: When a number is decreased by 20% the result is 48. decreased is subtraction This is EQUALS This is our unknown (x) This is 20% of our unknown (x).. So it will be .20x We then combine our like terms Since .80 is multiplying to our x- we must divide to obtain x alone. Does this make sense? When 60 is decreased by 20% the result is 48? Yes, that makes sense!

  14. Solve: When 3 times a number is increased by 5 , the result is 14. Find the number.

  15. When 3 times a number is increased by 5 , the result is 14. Find the number. We start this problem the same as we did the last one: When 3 times a number is increased by 5 , the result is 14. 3 times means multiplied by 3 This is our unknown (x) If we increase then it is plus 5 This is EQUALS again. We now solve this for x. We need combine like terms: subtract 5 on both sides We divide both sides by 3 to get x by itself Check your answer!

  16. Solve for x 6x-5=7+2x

  17. 6x -5=7+2x We start by combining our like terms: I am going to combine my x terms first. It doesn’t matter which you start with. • 6x -5=7+2x • -2x -2x • 4x -5 =7 • 4x=12 • X=3 Subtract 2x from both sides to combine x terms Add 5 to both sides to combine constant terms. • +5 +5 Divide both sides by 4 to obtain x by itself • 4 4

  18. Solve for x:

  19. We always work the parentheses first. They are prompting us to do the distributive property (5)(x)+(5)(4)=(7)(x)+(7)(-2) 5x+20=7x-14 +14 +14 5x + 34 = 7x -5x -5x 34=2x 2 2 17=x Add 14 to both sides to combine like terms Subtract 5x to both sides to combine like terms Divide by 2 to get x by itself.

  20. Solve for x 19-(2x+3)=2(x+3)+x

  21. 19-(2x+3)=2(x+3)+x We start this one like we did the last one: We always work the parentheses first. They are prompting us to do the distributive property again. Even though there is no constant in front of the first parentheses, we still have to distribute the negative sign (think of there being an invisible 1) • 19-(2x+3)=2(x+3)+x 19+(-1)(2x)+(-1)(3)=(2)(x)+(2)(3)+x 19-2x-3=2x+6+x 16-2x=3x+6 16=5x+6 10=5x 2=x We start by combining our like terms on the SAME side of the equals sign. Now we add 2x on both sides to combine our x terms. +2x +2x Now we subtract 6 on both sides to combine our constant terms -6 -6 Now divide by 5 on both sides to get x alone. 5 5

  22. Solve for x

  23. This is called a rational equation because it has rational expressions in it (fractions)! We always begin these by multiplying the whole equation by the Least Common Denominator. Our LCD is 24 in this case. 6,8, and 4 all go into 24. We can now reduce the numerator with the denominator. Now we use distributive property Now we can combine our like terms Hang in there!! Subtract 4x on both sides to combine x terms Add 21 to both sides to combine our constant terms Finally divide both sides by x to get x by itself

  24. Solve for x

  25. We multiply by the LCD again. In this case our LCD is (x-1) When we reduce, we see that quite a bit cancels! Whenever you have a rational equation and you multiply by the LCD- if you have done it right, there will be no more fractions. Distribute the 5 through So now we just solve this. Combine your like terms Add 4 to both sides Divide both sides by 5

  26. Good luck on your quiz!

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