If sx = 2x and tx = 3x, which value is equivalent to st = 7?

We have:

• s = 2x
• t = 3x

Now, we can express st as:

st = s * t = (2x) * (3x) = 6x²

We are given that st = 7. Thus, we can set up the equation:

6x² = 7

To find the value of x, we first divide both sides of the equation by 6:

x² = rac{7}{6}

Then, take the square root of both sides:

x = ±√(7/6)

Now, we can substitute this value of x back into the expressions for s and t if needed. However, in this case, we find that when st = 7, it requires calculating the values of 2x and 3x based on this x.

To recap, based on the equation we derived:

• The value of x can be expressed as ±√(7/6).
• Consequently, the expression for st is equivalent to 6x², which equals 7.

In summary, the equivalent value to st when st = 7 with the given equations is rooted in the relationship we established. This methodical approach allows us to conclude that while we can find x, the equivalency holds at the defined values of sx and tx.