Assuming the equation is:
[tex]\frac{x}{2}-\frac{10x-25}{10}=3(x+3)-(x-14)[/tex]
When fractions involve numeric denominators, the fractions can be removed by multiplying (both sides) by the LCM of the denominators.
Here the denominators are 2 and 10, hence the LCM is 10.
Multiply by 10 on both sides, not forgetting to distribute when multiplying on the right side:
[tex]10\frac{x}{2}-10\frac{10x-25}{10}=10*3(x+3)-10(x-14)[/tex]
simplify, remember that there are always implied parentheses around numerators and denominators:
[tex]5x-(10x-25)=30(x+3)-10(x-14)[/tex]
Now, distribute, i.e. remove parentheses and distribute:
5x-10x+25=30x+90-10x+140
Simplify
-5x+25=20x+230
transpose terms
25-230=20x+5x
solve
x=-205/25=-41/5
In this particular case, we can also take advantage of the term
(10x-25)/10=5(2x-5)/10=(2x-5)/2 which greatly simplifies the solution process, because the LCM will then be 2 instead of 10.
If we do that, the solution will be:
Multiply by 2 on both sides, not forgetting to distribute when multiplying on the right side:
[tex]\frac{x}{2}-\frac{10x-25}{10}=3(x+3)-(x-14)[/tex]
simplify, remember that there are always implied parentheses around numerators and denominators:
[tex]2\frac{x}{2}-2\frac{2x-5}{2}=2*3(x+3)-2(x-14)[/tex]
[tex]x-(2x-5)=6(x+3)-2(x-14)[/tex]
Now, distribute, i.e. remove parentheses and distribute:
[tex]x-2x+5=6x+18-2x+28[/tex]
Simplify
-x+5=4x+46
solve
5-46=4x+x
-41=5x
x=-41/5
with the same results.
x/2 - (10x - 25)/10 = 3(x + 3) - (x - 14)
Multiply each term by 10 to eliminate the fractions:-
5x - (10x - 25) = 30(x + 3) - 10(x - 14)
5x - 10x + 25 = 30x + 90 - 10x + 140
5x - 10x - 30x + 10x = 90 + 140 - 25
-25x = 205
x = -8.2 answer
