Solve the following equations

Question

Solve the following equations: 

a) 2x + 1=7

b) 2x - 9 =25

c) 5x - 20 = 3x - 8

d) 4r - r over 4 = 15 

and the r is above the 4 and the four is under a line! Sorry for that terrible description haha!

please help and show all working out!

thank you very much!

 

Answer 1

Hi Kath.  To solve equations, the number one thing to remember is: What you do to one side of an equal sign you must do to the other side.

 

a)

 

2x + 1 = 7

 

your goal here is to get x all by itself on the left side.  So, first subtract 1 to BOTH sides

 

2x + 1 = 7

     - 1    -1

 

2x = 6   

 

Now, to get rid of the 2 in front of the x (by the way, 2x means 2 times x), you must divide BOTH sides by 2.

 

2x = 6

2      2

 

Thus, you have your answer:

 

x = 3

 

 

b)

 

2x - 9 = 25   (add 9 to BOTH sides)

    +9     +9

 

2x = 34      (divide BOTH sides by 2)

 

 

x = 17

 

c)

 

5 x - 20 = 3x - 8    (first get x on the left side by subtracting 3x from BOTH sides)

-3x           -3x

 

2x - 20 = -8        (add 20 to BOTH sides)

     +20    +20

 

2x = 12    (divide BOTH sides by 2)

 

 

x = 6

 

 

d)

 

I think the problem is this:

 

4r - r    = 15

      4

 

Multiply all THREE terms by 4 to get rid of the fraction

 

16r - r = 60    (16r - r is 15r.......just think of r as 1r)

 

15r = 60   (divide BOTH sides by 15

 

r = 4

 

 

 

 

 

 

 

Answer 2

a 2x + 1 = 7

 

   2x = 6

 

    x = 3

 

b.  2x - 9 = 25

 

     2x = 34

 

       x = 17

 

c.  5x - 20 = 3x - 8

 

     5x = 3x - 8 + 20

 

      2x = 12

 

       x = 6