SOLUTION: Good morning I'm stuck with the following problems! 4/5x -3= 2 7a+8b=5c solve for a find the x intercept: 7x+5y=3 solve: 3(2-x)> x+2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Good morning I'm stuck with the following problems! 4/5x -3= 2 7a+8b=5c solve for a find the x intercept: 7x+5y=3 solve: 3(2-x)> x+2      Log On


   



Question 79237: Good morning I'm stuck with the following problems!

4/5x -3= 2


7a+8b=5c solve for a


find the x intercept: 7x+5y=3


solve: 3(2-x)> x+2

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Good morning I'm stuck with the following problems! 

                %284%2F5%29x+-+3+=+2 

Clear of fractions by multiplying every term by 5.
Use 5%2F1 to multiply by the first and use 
just 5 to multiply the other two terms by

            %285%2F1%29%284%2F5%29x+-+%285%293+=+%285%292

              4x - 15 = 10

Add 15 to both sides

                   4x = 25

Divide both sides by 4

                  %284x%29%2F4+=+25%2F4

                  x+=+25%2F4  


7a + 8b = 5c solve for a 

Isolate all terms with a on the left side.
Do this by subtracting 5b from both sides:

             7a = 5c - 8b

Draw a line under both sides and divide 
by 7

              %287a%29%2F7+=+%283c-8b%29%2F7}

Cancel the 7's on the left:
    
                a+=+%283c-8b%29%2F7}

Leave the answer just like that.

---------------------------------------

find the x intercept: 7x + 5y = 3 

To find the intercept for either letter
x or y, substitute 0 for the OTHER
letter and solve.

So we substitute 0 for the OTHER letter
y and solve for x.

       7x + 5y = 3
     7(0) + 5y = 3
        0 + 5y = 3
            5y = 3

Divide both sides by 5

            %285y%29%2F5+=+3%2F5

              y+=+3%2F5  

---------------------------------

solve: 3(2 - x) > x + 2

         6 - 3x > x + 2

Get rid of the x on the right by 
subtracting x from both sides:

        6 - 4x > 2

Get rid of the 6 on the left by 
subtracting 6 from both sides

          -4x > -4 

Divide both sides by -4 remembering
the rules:

1. When you divide (or multiply) 
   both sides of an inequality
   by a NEGATIVE number, you MUST
   reverse the sign of inequality.

2. When you divide (or multiply) 
   both sides of an inequality
   by a POSITIVE number, you DO NOT
   reverse the sign of inequality.

This is the first case, so we
reverse the sign of inequality:

             %28-4x%29%2F%28-4%29+%3C+%28-4%29%2F%28-4%29 
                
                x < 1

To write the solution is interval notation
we write:

               (-¥, 1)

Edwin