Question

What is 24minus 3/4X equals to four over X cube in a verbal expression?

A) Twenty-four minus three-fourths of X is equal to four divided by the cube of X.
B) Twenty-four times three-fourths of X equals four divided by X cubed.
C) Twenty-four subtracted from three-fourths of X is equal to four times X cubed.
D) Twenty-four divided by three-fourths of X is equal to four plus X cubed.

Answer 1

The verbal expression for the algebraic equation '24 - (3/4)X = 4/X^3' is 'Twenty-four minus three-fourths of X is equal to four divided by the cube of X.' Understanding negative exponents and their application is crucial to solving such equations.

Step-by-step explanation:

The expression 24 minus 3/4 of X equals four over the cube of X can be interpreted verbally as "Twenty-four minus three-fourths of X is equal to four divided by the cube of X." This describes an algebraic equation where 24 is being subtracted by the fraction 3/4 multiplied by X, and the result is equal to the quotient of 4 and the cube of X (expressed as X to the power of negative three).

Understanding the properties of exponents is key here. For instance, a negative exponent denotes that the base is in the denominator, so X to the power of negative three is equivalent to 1 divided by X3, which is the cube of X. This is based on the rule that xn where n is negative can be written as 1/x-n or, in other words, x-n = 1/xn. Similarly, if we are considering scales or proportions like 1:4 or 32 ∙ 35, we are still employing multiplication, division, and the laws of exponents—showing that understanding these concepts is crucial for solving algebraic equations.