Final answer:
To find the value of x that makes the statement true, simplify the expression on the left side of the equation and set it equal to 4/3. Cross multiply to eliminate the fractions and solve for x. The value of x is approximately 3.34.
Step-by-step explanation:
To find the value of x that makes the statement true, we need to simplify the expression on the left side of the equation. Start by multiplying the numerators and denominators together separately: (3x7/11 * 11/5) / (3/7 * x). This simplifies to (21/11) / (3x/7). Next, divide the fraction by a fraction by multiplying the numerator by the reciprocal of the denominator: (21/11) * (7/3x). This simplifies to (147/33x). Now that we have a single fraction, set it equal to 4/3 and solve for x.
147/33x = 4/3
Now, cross multiply to eliminate the fractions: 147 * 3 = 33x * 4
Solve for x: 441 = 132x
Divide both sides by 132: x = 441/132
Simplify the fraction: x = 3.34
So, the value of x that makes the statement true is approximately 3.34.