Question

Find the value of k that will make the following two expressions equivalent

-10.5x + k and -2.1(5x - 3.7) + 4.1

Answer 1

The value of k that makes the expressions equivalent is 11.87, found by expanding the second expression and equating it to the first.

Step-by-step explanation:

To find the value of k that makes the expressions -10.5x + k and -2.1(5x - 3.7) + 4.1 equivalent, we must first expand the second expression and then solve for k.

Expanding the second expression gives us:

• -2.1 * 5x = -10.5x
• -2.1 * (-3.7) = 7.77
• So, the expanded form is -10.5x + 7.77 + 4.1

Combining like terms in the expanded expression, we get:

• 7.77 + 4.1 = 11.87
• The expression now is -10.5x + 11.87

The expressions are equivalent when the constant terms are equal, so:

• k = 11.87

Therefore, the value of k that makes the two expressions equivalent is 11.87.