Q: How do you solve: 5/7 (x – 70) + 3/7 = 0?
A: There are many different ways to solve this problem, and all will lead you to the same answer. I am going to show two methods:
Method 1
Solve as you normally would:
5/7 (x – 70) + 3/7= 0
Subtract 3/7 from both sides:
5/7 (x – 70) + 3/7 -3/7 = 0 -3/7
5/7 (x – 70) = -3/7
Multiply the 5/7 through to the (x – 70) like so:
5/7*x – 5/7 * 70 = -3/7
5/7x – 350/7 = -3/7
Even though -350/7 can be reduced, I am going to wait to do that…
So,
5/7x – 350/7 = -3/7
Now add 350/7 to both sides:
5/7x – 350/7 + 350/7 = -3/7 + 350/7
5/7x = 347/7
Now, the final step to get x by itself is to multiply by the reciprocal of 5/7, which is 7/5… Doing this will clear the fraction:
(7/5) * 5/7x = 347/7 *(7/5)
35/35x = 347*7/(7*5)
x = 347*7/(7*5) [cancel a 7 out of the top and out of the bottom]
x = 347/5
Method 2
Clear the fraction first. Since “7” is the only denominator, multiply everything by 7:
5/7 (x – 70) + 3/7= 0
7 * [ 5/7 (x – 70) + 3/7= 0 ]
Distribute the “7” through to each term like so:
7*(5/7)(x – 70) + 7(3/7) = 7 *0
Simplify the fractions… Notice we can cancel out most of the 7’s:
7*(5/7)(x – 70) + 7(3/7) = 7 *0
5(x – 70) + 3 = 0
Now, no more fractions! Distribute the 5 through:
5x – 350 + 3 = 0
Simplify:
5x – 347 = 0
5x = 347
x = 347/5