Question

13/14x-4/21x+1/7x=2 1/3

Answer 1

Ответ:

$x=2\frac{24}{37}$

Пошаговое объяснение:

$\frac{13}{14}x-\frac{4}{21}x+\frac{1}{7}x=2\frac{1}{3}\\\\\frac{13\cdot3}{14\cdot3}x-\frac{4\cdot2}{21\cdot2}x+\frac{1\cdot6}{7\cdot6}x=\frac{7}{3}\\\\\frac{39}{42}x-\frac{8}{42}x+\frac{6}{42}x=\frac{7}{3}\\\\\frac{37}{42}x=\frac{7}{3}\ \ \ |:\frac{37}{42}\\\\x=\frac{7}{3}\cdot\frac{42}{37}\\\\x=\frac{98}{37}\\\\x=2\frac{24}{37}$

Answer 2

To solve the equation (13/14)x - (4/21)x + (1/7)x = 2 1/3, you'll need to combine like terms and isolate x on one side of the equation. Here are the steps to do that:

1. Combine the x terms on the left-hand side of the equation: (13/14)x - (4/21)x + (1/7)x = 2 1/3

   To combine these fractions with different denominators, find a common denominator, which is the least common multiple (LCM) of 14, 21, and 7, which is 42.

2. Rewrite each fraction with a common denominator of 42: (13/14)x * (3/3) - (4/21)x * (2/2) + (1/7)x * (6/6) = 2 1/3

   Now, the equation becomes: (39/42)x - (8/42)x + (6/42)x = 2 1/3

3. Add the fractions on the left-hand side: [(39/42) - (8/42) + (6/42)]x = 2 1/3

   Combine the fractions: (37/42)x = 2 1/3

4. Now, let's convert 2 1/3 into an improper fraction. To do that, multiply the whole number (2) by the denominator (3) and then add the numerator (1): 2 * 3 + 1 = 6 + 1 = 7

   So, 2 1/3 is equivalent to 7/3.

5. Substitute this back into the equation: (37/42)x = 7/3

6. To isolate x, divide both sides of the equation by (37/42): x = (7/3) / (37/42)

7. When you divide by a fraction, it's the same as multiplying by its reciprocal (flipping it): x = (7/3) * (42/37)

8. Multiply the fractions on the right-hand side: x = (7 * 42) / (3 * 37)

9. Calculate the numerator and denominator separately: x = (294) / (111)

10. Simplify the fraction if possible: x = 2.6486486486486487 (rounded to several decimal places)

So, the solution to the equation is approximately x ≈ 2.6486.