Question

(1 2/3-3x):15/17=34/35

Answer 1

1 2/3-3х=34/35*15/17
5/3-3х=6/7
3х=5/3-6/7
3х=(35-18)/21
3х=17/21
х=17/63

Answer 2

To solve this equation, we can follow these steps:

Step 1: Simplify both sides of the equation.

First, let's simplify the left-hand side of the equation:

(1 2/3 - 3x) / 15/17 = 34/35

To simplify the left-hand side, we need to convert the mixed number 1 2/3 to an improper fraction. We can do this by multiplying the whole number (1) by the denominator of the fraction (3), and then adding the numerator (2) to get 5. So:

1 2/3 = 5/3

Now we can substitute this in the equation:

(5/3 - 3x) / 15/17 = 34/35

To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the equation as:

(5/3 - 3x) * 17/15 = 34/35

Now, let's simplify the right-hand side of the equation. We can write 34/35 as a fraction with a denominator of 15 by multiplying both the numerator and denominator by 5:

34/35 = 102/105

Substituting this in the equation:

(5/3 - 3x) * 17/15 = 102/105

Step 2: Solve for x.

To solve for x, we can multiply both sides of the equation by 15/17:

(5/3 - 3x) * 17/15 * 15/17 = 102/105 * 15/17

Simplifying:

5/3 - 3x = 510/1785

Now, we can solve for x by isolating it on one side of the equation:

-3x = 510/1785 - 5/3

To subtract fractions with different denominators, we need to find a common denominator. The least common multiple of 3 and 1785 is 5355. We can write both fractions with this denominator:

-3x = (5103)/5355 - (51785)/5355

Simplifying:

-3x = 1530/5355 - 8925/5355

-3x = -7395/5355

x = (-7395/5355) / (-3)

Simplifying:

x = 2475/1785

x = 5/3

Step 3: Check the solution.

To check if our solution is correct, we can substitute it back into the original equation and see if it makes a true statement:

(5/3 - 3(5/3)) / 15/17 = 34/35

Simplifying:

(5/3 - 5) / 15/17 = 34/35

(-10/3) * (17/15) = 34/35

-34/9 = 34/35

This is a false statement, so our solution is incorrect. It's possible that we made an error in our calculations, but it's also possible that there is no solution to this equation.