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In this problem, a, b, c, and d are nonzero integers. If a/b is added to x, the sum is c/d . Which statement can be used to prove that z must be a rational number?
In this problem, a, b, c, and d are nonzero integers. If a/b is added to x, the sum is c/d . Which statement can be used to prove that z must be a rational number? a. x= (c+a)/d-b
b. x= (c-a)/d-b
c. x= (cb+ad)/bd
d. x= (cb-ad)/bd
Final answer:Statement d, x = (cb - ad) / bd, is the correct representation of the given algebraic equation that proves z is a rational number. It shows x as the result of subtraction between two rational numbers, which results in another rational number.Therefore the correct option is d.Explanation:The problem states that whena/bis added tox, the sum isc/d. We need to identify which statement would prove thatzmust be a rational number. The sum in algebraic terms would be:x + a/b = c/d. To solve forx, we need to isolate it on one side of the equation. Hence, we rewrite the equation as:x = c/d - a/b.To combine the two fractions, they require a common denominator. The common denominator ofbanddis their product, bd, so we need to rewrite the fractions:x = (cb - ad) / (bd)Thus, the correct statement from the given options that would provezis a rational number is:d. x = (cb - ad) / bdStatement d explains thatxis indeed a rational number because it is expressed as a ratio of two integers, which is the definition of a rational number....