- 3/4x = 2/7
x= -8/21?
and 2 2/5x = 8/15
x=2/9?
Both of your answers are correct.
To solve the equation 3/4x = 2/7:
Step 1: Multiply both sides of the equation by the reciprocal of the coefficient of x on the left side, which in this case is 4/3. This eliminates the fraction on the left side, giving us:
(4/3) * (3/4x) = (4/3) * (2/7)
1x = 8/21
So, x = 8/21.
To solve the equation 2 2/5x = 8/15:
Step 1: Convert the mixed number on the left side to an improper fraction. 2 2/5 can be written as 12/5.
Now we have:
(12/5)x = 8/15
Step 2: Multiply both sides of the equation by the reciprocal of 12/5, which is 5/12. This eliminates the fraction on the left side, giving us:
(5/12) * (12/5x) = (5/12) * (8/15)
1x = 2/9
So, x = 2/9.
To verify if the given values for x are correct, let's solve each equation step by step:
1. - 3/4x = 2/7
To isolate x, we need to get rid of the fraction on the left side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction, which is 4/3:
(4/3)(-3/4x) = (4/3)(2/7)
Simplifying, we get:
(1)(x) = 8/21
Hence, x = 8/21.
Therefore, the given value x = -8/21 is incorrect.
2. 2 2/5x = 8/15
To solve for x, we first need to convert the mixed number on the left side of the equation into an improper fraction. To do this, we multiply the whole number (2) by the denominator (5) and add the numerator (2):
(2 * 5 + 2)/5x = 8/15
(12/5)x = 8/15
Now we can isolate x by multiplying both sides of the equation by the reciprocal of the fraction, which is 5/12:
(5/12)(12/5x) = (5/12)(8/15)
Simplifying, we get:
(1)(x) = 2/9
Hence, x = 2/9.
Therefore, the given value x = 2/9 is correct.