((3x+4)/2)+1=(5x+10)/8

Question

Please explain the steps

Answer 1

(3x+4) / 2 + 1 = (3x+4)/2 + 2/2 = (3x+6) / 2

So, we have (3x+6) / 2 = (5x + 10) / 8

Cross multiply to get 8(3x + 6) = 2(5x + 10)

24x + 48 = 10x + 20

14x = -28

x = -2

Answer 2

Mark's answer is perfect, just thought I'd show a different way.

3x + 4 + 1 = 5x + 10

2 8

There are multiple ways to solve this; another way of solving it is to get rid of the fractions by multiplying everything by the LCD. The LCD, least common denominator, is the smallest number that both denominators will go into. I.e., what's the smallest number that 2 and 8 go into? 8!

So now we multiply EVERYTHING (all three terms) by the LCD of 8.

8(3x + 4) + 8(1) = 8(5x + 10)

2 8

Remember, though, that the point of this was to get rid of the fractions. So rather than multiplying, let's simply each fraction.

4(3x + 4) + 8(1) = 1(5x + 10) ← For the first term, 8 / 2 simplifies to 4. For the third term, 8 / 8 simplifies to 1.

Now we can go ahead and multiply.

12x + 16 + 8 = 5x + 10

12x + 24 = 5x + 10 ← Combine "easy" like terms (i.e., like terms that are on the same side of the equal sign.)

And now let's deal with the "harder" like terms (those on opposite sides of the equation) by subtracting them from both sides:

12x + 24 = 5x + 10

- 5x -5x

7x + 24 = 10

- 24 -24

7x = -14

Finally, we have a one-step equation. Just divide both sides by 7.

7x = -14

7 7

x = -2

Hope this helps too!

Andrés