having problems solving problems step by step (equations algebraically) and really need some help on this issue

Question

t and 2 3rds = 4

5 sqrt x+ 1 = 3

2/3 =2 - 5x-3 over x-1

 

Answer 1

I am not sure if I have your equations correct, so please correct me if any of these are set up wrong.

1.  t + 2/3= 4                  Given

t + 2/3 - 2/3 = 4 - 2/3     Subtract 2/3 from each side

t = 10/3                         Simplify

 

2.  5√(x + 1) = 3             Given

5√(x + 1)/5 = 3/5            Divide each side by 5

√(x + 1) = 3/5                 Simplify

x + 1 = (3/5)²                  Square both sides

x + 1 = 9/25                    Simplify

x + 1 - 1 = 9/25 - 1          Subtract 1 from each side

x = - 16/25                      Simplify

 

3.  2/3 = 2 - (5x - 3)/(x - 1)          Given

2/3 - 2 = 2 - (5x - 3)/(x - 1) - 2    Subtract 2 from each side

-4/3 = -(5x - 3)/(x - 1)                 Simplify

-4/3(x - 1) = -(5x - 3)                  Multiply both sides by x - 1

-4/3x + 4/3 = -5x + 3                  Distribute the -4/3 on the left and the - on the right

-4/3x + 4/3 + 5x = 3                   Add 5x to each side

11/3x + 4/3 = 3                          Simplify

11/3x = 3 - 4/3                           Subtract 4/3 from each side

11/3x = 5/3                                Simplify

x = 5/3 * (3/11)                         Multiply both sides by 3/11

x = 5/11                                    Simplify