Question

question 5 (multiple choice worth 5 points) (04.04r mc) solve for x: \\(\frac{2}{3} = \frac{x - 1}{5}\\) options: \\(\frac{7}{3}\\), \\(\frac{11}{3}\\), \\(\frac{13}{3}\\), 3

Explanation:

Step1: Cross - multiply the equation

Given the equation $\frac{2}{3}=\frac{x - 1}{5}$, cross - multiplying (which is based on the property of proportions: if $\frac{a}{b}=\frac{c}{d}$, then $a\times d=b\times c$) gives us $2\times5 = 3\times(x - 1)$.
So, $10=3(x - 1)$.

Step2: Distribute the 3 on the right - hand side

Using the distributive property $a(b + c)=ab+ac$ (here $a = 3$, $b=x$, $c=-1$), we get $10 = 3x-3$.

Step3: Solve for x

First, add 3 to both sides of the equation: $10 + 3=3x-3 + 3$.
This simplifies to $13 = 3x$.
Then, divide both sides by 3: $x=\frac{13}{3}$.

Answer:

$\boldsymbol{\frac{13}{3}}$