Help on 1&2 please!!

1. 25

2. 7

Step-by-step explanation:

Let the variables be denoted as "x".

1. If 5 times "x" is increased by 50, the result is the same as when 200 is decreased by "x".

Set the equation:

5x + 50 = 200 - x

Isolate the x. Note the equal sign, what you do to one side, you do to the other. First, add x and subtract 50 from both sides:

5x (+ x) + 50 (-50) = 200 (-50) - x (+x)

5x + x = 200 - 50

6x = 150

Next, divide 6 from both sides of the equation:

(6x)/6 = (150)/6

x = 150/6 = 25

25 is your number.

~

2. If 50 is decreased by 4 times "x", the result is 15 more than "x".

Set the equation:

50 - 4x = 15 + x

Isolate the x. Note the equal sign, what you do to one side, you do to the other. First, subtract x and subtract 50 from both sides:

50 (-50) - 4x (-x) = 15 (-50) + x (-x)

-4x - x = 15 - 50

-5x = -35

Divide -5 from both sides of the equation:

(-5x)/-5 = (-35)/-5

x = -35/-5 = 7

x = 7

7 is your number.

~

#1) x=25, #2) x=7

Step-by-step explanation:

Number One:

We will replace this "number" with the variable "x".

"5 times a number.." gives us 5x.

"...increased by 50" gives us 5x+50.

5x+50

"The result is the same as when 200 is decreased by the number." gives us 200-x.

Now, we have a complete equation.

5x+50=200-x

1) To solve this, first subtract 50 from both sides.

     5x=150-x

2) Add the x on both sides.

     5x+x=150

3) Combine like terms.

    6x=150

4) Divide by 6 on both sides.

   x=25

Number Two:

Once again, lets use "x" as the number.

"If 50 is decreased by 4 times a certain number..." gives us 50-4x.

"...the result is 15 more than the number." gives us x+15.

Now, we have another complete equation! :)

50-4x=x+15

1) Subtract 15 from both sides.

    35-4x=x

2) Add 4x to both sides.

    35=x+4x

3) Combine like terms.

    35=5x

4) Divide by 5 on both sides.

    x=7

That's it! I hope this helped :)