Solve and verify 7/x+35=1/10
Not much to this one.
1/10 = 7/70
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To solve the equation (7/x) + 35 = 1/10, we need to isolate the variable x.
Step 1: Subtract 35 from both sides of the equation:
(7/x) = 1/10 - 35
Step 2: Simplify the right side of the equation:
(7/x) = 1/10 - 350/10
To combine the fractions, we need a common denominator. The denominator of 10 can be used for both fractions.
Step 3: Convert both fractions into fractions with the common denominator of 10:
(7/x) = (1 - 350) / 10
Simplifying further:
(7/x) = (-349) / 10
Step 4: Cross-multiply:
(-349) * x = (7) * 10
Simplifying further:
-349x = 70
Step 5: Divide both sides of the equation by -349 to solve for x:
x = 70 / (-349)
To verify the solution, we substitute the obtained value of x back into the original equation:
(7/x) + 35 = 1/10
Plugging in the value of x = 70 / (-349):
(7 / (70 / (-349))) + 35 = 1/10
Simplifying further:
(7 * (-349) / 70) + 35 = 1/10
-349/10 + 35 = 1/10
(-349 + 350) / 10 = 1/10
1/10 = 1/10
Since the left side equals the right side, we can conclude that the solution x = 70 / (-349) is verified.