# Find the value of the variable x in the following proportions: A) 6/x = 9/8 B) 5/5 = 4/x C) 1/2 =...

## Question:

Find the value of the variable {eq}x {/eq} in the following proportions:

A) {eq}\frac{6}{x} = \frac{9}{8} {/eq}

B) {eq}\frac{5}{5} = \frac{4}{x} {/eq}

C) {eq}\frac{1}{2} = \frac{2}{x} {/eq}

D) {eq}\frac{x}{10} = \frac{10}{8} {/eq}

## Algebra:

Algebra is a branch of mathematics that involves writing the unknown values as variables in an equation and then using the algebra rules to solve for the unknown variables.

A) {eq}\frac{6}{x} = \frac{9}{8}{/eq}

To solve for x, we must simplify the equation until we are left with only the variable on one side of the equation keeping in mind that whatever we do on the RHS of the equation must also be done on the LHS of the equation.

Let's start by multiplying both sides of our equation by x.

• {eq}\dfrac{6}{x}\times x = \dfrac{9}{8}\times x{/eq}
• {eq}6 = \dfrac{9}{8}\times x{/eq}

Next, we will divide both sides of the equation by 9/8.

• {eq}6\div \dfrac{9}{8} = \dfrac{9/8}{9/8}\times x{/eq}
• {eq}6\times \dfrac{8}{9} =x{/eq}
• {eq}x = \dfrac{48}{9} = \boxed{\dfrac{16}{3}} {/eq}

B) {eq}\frac{5}{5} = \frac{4}{x}{/eq}

• {eq}\dfrac{5}{5} = \dfrac{4}{x}{/eq}

The LHS is equal to 1 since a number divided by itself is equal to 1.

• {eq}1= \dfrac{4}{x}{/eq}

Multiplying both sides of the equation by x, we have:

• {eq}1\times x= \dfrac{4}{x}\times x{/eq}
• {eq}x = \boxed{4} {/eq}

C) {eq}\frac{1}{2} = \frac{2}{x}{/eq}

• {eq}\frac{1}{2} = \frac{2}{x}{/eq}

Multiplying both sides of the equation by x:

• {eq}\dfrac{1}{2} \times x = \dfrac{2}{x}\times x{/eq}
• {eq}\dfrac{1}{2} x = 2{/eq}

The next step is to multiply both sides of the equation by 2.

• {eq}2\times \dfrac{1}{2} x = 2\times 2{/eq}
• {eq}x = \boxed{4} {/eq}

D) {eq}\dfrac{x}{10} = \dfrac{10}{8}{/eq}

In this equation, the operation that leaves the unknown x on one side of the equation is to multiply both sides of the equation by 10.

• {eq}\dfrac{x}{10}\times 10 = \dfrac{10}{8}\times 10 {/eq}
• {eq}x = \dfrac{100}{8} = \boxed{ \frac{25}{2} } {/eq}