Question

X/4+5=x/3+10 Solve and check.

Answer 1

X/4 + 5 = x/3 + 10

x/4 - x/3 = 10 - 5

(3x -4x)/12 = 5

-x/12 = 5

-x = 12 *5

-x = 60

x = -60.

Check:
Left Hand side, LHS:
x/4 + 5

-60/4 + 5 =  -15 + 5 = 5- 15 = -10

Right Hand side, RHS:
x/3 + 10

-60/3 + 5 =  -20 + 10 = 10- 20 = -10

-10 = -10
LHS = RHS

Answer 2

So,

$\frac{x}{4} +5= \frac{x}{3} +10$

To get rid of the fractions, find the LCM of the denominators.

LCM of 4, 3 = 12

Multiply both sides by 12.

3x +60= 4x +120

Subtract 3x from both sides.
60 = x + 120

Subtract 120 from both sides.
x = -60


Check.

$\frac{-60}{4} +5= \frac{-60}{3} +10$

-15 + 5 = -20 + 10

-10 = -10

This checks.

S = {-60}