Question

4 + (х+3)/16 = 3/7 - 6/15

Answer 1

$\displaystyle \tt 4+\frac{x+3}{16}=\frac{3}{7}-\frac{6}{15}\\\displaystyle \tt 4+\frac{x+3}{16}=\frac{1}{35} \: \: \: \: | \cdot560\\\displaystyle \tt 4+\frac{x+3}{16}=\frac{3}{7}-\frac{6}{15}\\2240+35(x+3)=16\\\displaystyle \tt 2240+35x+105=16\\\displaystyle \tt 2345+35x=16\\\displaystyle \tt 35x=16-2345\\\displaystyle \tt 35x=-2329\\\displaystyle \tt x=-\frac{2329}{35}\\\displaystyle \tt x=-66\frac{19}{35}$

Answer 2

To solve the equation, let's first simplify both sides step by step:

1. Start with the equation: 4 + (x + 3) / 16 = 3 / 7 - 6 / 15

2. Find a common denominator for the fractions on the right side, which is 15 (the least common multiple of 7 and 15):

   3/7 = (3 * 15) / (7 * 15) = 45 / 105 6/15 = (6 * 7) / (15 * 7) = 42 / 105

   The equation becomes: 4 + (x + 3) / 16 = (45 - 42) / 105

3. Simplify the right side further: (45 - 42) / 105 = 3 / 105

   The equation becomes: 4 + (x + 3) / 16 = 3 / 105

4. Now, eliminate the fraction on the left side by multiplying both sides by 16:

   16 * (4 + (x + 3) / 16) = 16 * (3 / 105)

   Simplify: 4 + x + 3 = 3 * (16 / 105)

5. Continue simplifying: x + 7 = 48 / 105

6. Subtract 7 from both sides to isolate x:

   x = 48 / 105 - 7

7. To express the result as a simplified fraction, find a common denominator for 105 and 7 (which is 105):

   x = (48 - 735) / 105

   Since 48 is smaller than 105, the fraction cannot be simplified further.

So, the solution for the equation is: x = (48 - 735) / 105 x = -687 / 105