Problem: 6-x/3=4(x+1)/7
How do I solve this equation?
6 - x/3 = 4(x + 1)/7
6 - x/3 = (4x + 4)/7
6 - x/3 = 4x/7 + 4/7
6 - x/3 - 4x/7 = 4x/7 + 4/7 - 4x/7
6 - x/3 - 4x/7 = 4/7
6 - x/3 - 4x/7 - 6 = 4/7 - 6
-x/3 - 4x/7 = 4/7 - 6
Common denominators on the left side. Also, fractions on the right.
-7x/21 - 12x/21 = 4/7 - 42/7
-19x/21 = -38/7
Eliminate the fractions.
(-19x/21) * 21 = (-38/7) * 21
-19x = -114
-19x/-19 = -114/-19
x = 6
Check it.
6 - x/3 = 4(x + 1)/7
6 - 6/3 = 4(6 + 1)/7
6 - 2 = 4(7)/7
4 = 4 * 7/7
4 = 4 * 1
4 = 4
Answer: x = 6