Practice problems #3?

Question

I need help on the following problems, and all steps and formulas would greatly needed:

1. 3/4 + 1/6-2/3

2. 8-3(5-3^2)

___________

7-2x6

3. 2/5x+1/6=-2/3

How to graph linear equations?

4. y= -1/2x +4

5. 4x-5y=15

Answer 1

1. 3/4 + 1/6 - 2/3

To add/subtract fractions, they need to have the same denominator:

The least common multiple of 4, 6, and 3 is 12.

3/4 = 9/12

1/6 = 2/12

2/3 = 8/12

3/4 + 1/6 - 2/3

= 9/12 + 2/12 - 8/12

= 3/12

= 1/4

2. Remember this:

Please Excuse My Dear Aunt Sally

This will help you remember the order of operations:

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

A) First calculate what's inside the parentheses:

     1) Deal with the exponent

8-3(5-3^2)             8 - 3(5 - 9)

___________ =  ____________

7-2x6                   7 - 2 * 6

     2) Subtract 9 from 5

8-3(5-9)              8-3(-4)

___________ = _________

7-2*6                  7-2*6

B) Multiply from left to right in the numerator and in the denominator:

8 - 3(-4)      8 + 12

_______ = _______

7 - 2*6        7 - 12

C) Add/Subtract in the numerator and in the denominator:

8 + 12         20

______ = ________

7 - 12          -5

D) Divide 20 by -5

20      

___ = -4

-5

3. (2/5)x + 1/6 = -2/3.  Subtract 1/6 from both sides of the equation:

(2/5)x = -(2/3) - (1/6).  Fractions should have the same denominator in order to subtract them:

(2/5)x = (-4/6) - (1/6)

(2/5)x = -5/6. Multiply both sides by (5/2) to isolate x:

x = (-5/6) * (5/2)

x = -25/12

4. The equation is in slope-intercept form.  4 is the y-intercept and -1/2 is the slope.  

Since 4 is the y-intercept (where the line crosses the y-axis), one point that the line goes through is (0, 4).

Using the slope, you can count 1 square down and 2 squares to the right on the graph to find the next point, or 1 up and 2 to the left.

From that point, count 1 down and 2 to the right (or 1 up and 2 to the left) again to get the next point.  Do this until you have enough points through which you draw a line.

OR

you can just construct a table of x and y values.

Pick some values for x, and then solve for y.  Plot the points you get on the graph.  And then draw a line through those points.

5. The equation is in standard form.  It will be easier to find points to graph if it were in slope-intercept form like #4.  To change it into slope-intercept form, solve the equation for y:

4x - 5y = 15

-5y = -4x + 15

y = (4/5)x - 3

Here, the y-intercept is -3, so one point on the graph is (0, -3).  The slope is (4/5).  So from (0, -3) you would go up 4 and 5 to the right, etc.

or you can construct a table of values.

Hope that helped!