Question

solve for x in each of the following proportions.
a. \\(\frac{8}{x} = \frac{40}{35}\\) b. \\(\frac{x}{4} = \frac{-3}{11}\\)
c. \\(\frac{5}{6} = \frac{4x}{121}\\) d. \\(2\frac{1}{2}\\) is to 4 as x is to 20
a. x = \\(\square\\) (simplify your answer. type an integer, proper fraction, or mixed number.)
b. x = \\(\square\\) (simplify your answer. type an integer, proper fraction, or mixed number.)
c. x = \\(\square\\) (simplify your answer. type an integer, proper fraction, or mixed number.)
d. x = \\(\square\\) (simplify your answer. type an integer, proper fraction, or mixed number.)

Explanation:

Part a

Step1: Cross - multiply the proportion

Given \(\frac{8}{x}=\frac{40}{35}\), cross - multiplying gives \(40x = 8\times35\).

Step2: Simplify the right - hand side

Calculate \(8\times35=280\), so the equation is \(40x = 280\).

Step3: Solve for x

Divide both sides by 40: \(x=\frac{280}{40}=7\).

Step1: Cross - multiply the proportion

Given \(\frac{x}{4}=\frac{-3}{11}\), cross - multiplying gives \(11x=4\times(-3)\).

Step2: Simplify the right - hand side

Calculate \(4\times(-3)=-12\), so the equation is \(11x=-12\).

Step3: Solve for x

Divide both sides by 11: \(x =-\frac{12}{11}\).

Step1: Cross - multiply the proportion

Given \(\frac{5}{6}=\frac{4x}{121}\), cross - multiplying gives \(6\times4x = 5\times121\).

Step2: Simplify both sides

Simplify the left - hand side to \(24x\) and the right - hand side to \(605\), so the equation is \(24x = 605\).

Step3: Solve for x

Divide both sides by 24: \(x=\frac{605}{24}\).

Answer:

\(x = 7\)

Part b