(x – 7)/5 – 5/2 = (x + 9)/10?

Question

help please...

Answer 1

To make this easier, let's move the (x+9)/10 term to the left side of the equation. Since you're changing the side of the equation that the term is on, you also have to change the sign of the number. So, your equation is now the following:

(x-7)/5 - (x+9)/10 - 5/2 = 0

Now, I personally feel that it's much easier to move the -5/2 term to the other side of the equation. So, if we do that, we have to change the sign of the number. So, your equation is now the following:

(x-7)/5 - (x+9)/10 = 5/2

Now, we have to find the common denominator for all three numbers. This would be the LCM (Least Common Multiple) of the three denominators. The numbers are 5, 10 and 2. The LCM of those numbers must be 10, because 2, 5 and 10 all go into 10, and there is no smaller number that all these numbers go into, logically. So, we make all denominators 10 now. And, as a rule of mathematics, whatever you multiply by the denominator you have to multiply by the numerator.

(2(x-7))/10 - (x+9)/10 = 25/10

Now, since on the left side of the equation both terms have the same denominator, the numerators of both terms, logically, can be put as one numerator with the denominator as 10. Look:

(2(x-7) - (x+9))/10 = 25/10

Now that both sides of the equation have a denominator of 10, we can eliminate the denominators, logically, and our equation is now:

2(x-7) - (x+9) = 25

Now let's multiply 2 by (x-7).

2x-14 - (x+9) = 25

Now we negate the term (x+9), since there's a negative sign in front of it; since it's in parenthesis, we negate both the x and the 9. So we have:

2x-14-x-9=25

Now we add the like x terms and constants and get:

x-23=25

Now, adding 23 to both sides we isolate x and get:

x= 25+23

Simplifying we get:

x=48

So the answer is:

x=48.

There you go. I'm glad I could help. :)

Answer 2

(x – 7)/5 – 5/2 = (x + 9)/10
[2(x-7)-5(5)]/10 = (x+9)/10
2(x-7)-5(5)= (x+9)
2x -14 -25 = x+9
x = 48

Answer 3

Cross multiply. (x-7)/5-5/2=(x+9)/10.
2x-14-25=x+9
x=48

Answer 4

First simplify the left side.
Find a common denominator.

(2(x-7)-5*5)/10=(x+9)/10

Multiply both sides by ten to get rid of the fractions.

2(x-7)-25=x+9

Distribute the 2.

2x-14-25=x+9

Solve for x.

2x-39=x+9
x=48

Answer 5

(x – 7)/5 – 5/2 = (x + 9)/10

First multiply bot sides by 10

2(x - 7) - 5(5) = (x + 9)
2x - 14 - 25 = x + 9
x = 48

Answer 6

Multiply both sides by 10:
2(x-7)-25=x+9
2x-14-25=x+9
2x-39=x+9
x-39=9
x=48

Check:
(48-7)/5-5/2=(48+9)/10
41/5-5/2=57/10
82/10-25/10=57/10
57/10=57/10

I hope this helps!

Answer 7

(x – 7)/5 – 5/2 = (x + 9)/10

10[(x – 7)/5 – 5/2] = [(x + 9)/10]10

2(x-7)-25=x+9

2x-14-25=x+9

2x-x=9+39

x=48

Answer 8

Mult by 10

2(x-7) - 5(5) = x+9

2x - 14 - 25 = x+9

2x - 39 = x+9

x = 48

Answer 9

Using the lcd as 10 we can start

2(x-7)-25=x+9
2x-14-25=x+9
2x-39=x+9
2x-39+39=x+39
2x=x+48
2x-x=x-x+48
x=48