Final answer:
To solve the equation '2 2/7 ÷ (0.6x) = 4/21 ÷ 0.25', convert 2 2/7 to an improper fraction, rewrite 4/21 ÷ 0.25 as 4/21 x 4, simplify both sides of the equation, cross-multiply, and solve for x.
Step-by-step explanation:
To solve the equation '2 2/7 ÷ (0.6x) = 4/21 ÷ 0.25', we can start by simplifying both sides of the equation. On the left side, 2 2/7 can be converted to an improper fraction, which is 16/7. On the right side, 4/21 ÷ 0.25 can be rewritten as 4/21 x 4. Since division by a fraction is the same as multiplying by its reciprocal, we can rewrite the equation as (16/7) ÷ (0.6x) = 4/21 x 4.
To simplify further, we can divide both sides of the equation by 4. This gives us the equation (16/7) ÷ (0.6x) = 1/21.
Next, we can cross-multiply. This means multiplying the numerator of one fraction by the denominator of the other fraction. For example, cross-multiplying (16/7) ÷ (0.6x) and 1/21 results in (16/7) x 21 = (0.6x) x 1.
Simplifying the left side of the equation, we get (16/7) x 21 = 336/7. And simplifying the right side, we get (0.6x) x 1 = 0.6x.
Our equation is now 336/7 = 0.6x. To solve for x, we can multiply both sides of the equation by 7/336. This will cancel out the 336/7 on the left side and give us x on the right side: x = (336/7) x (7/336) = 336/2352 = 0.1429.