Question

1. \\(\frac{5}{17} = \frac{19}{x + 4}\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation $\frac{5}{17}=\frac{19}{x + 4}$, by the cross - multiplication property of proportions (if $\frac{a}{b}=\frac{c}{d}$, then $a\times d=b\times c$), we get $5\times(x + 4)=17\times19$.

Step2: Expand the left - hand side and calculate the right - hand side

Expand the left - hand side: $5x+20$. Calculate the right - hand side: $17\times19 = 323$. So the equation becomes $5x+20 = 323$.

Step3: Isolate the term with $x$

Subtract 20 from both sides of the equation: $5x=323 - 20$. Calculate $323-20 = 303$, so $5x = 303$.

Step4: Solve for $x$

Divide both sides of the equation by 5: $x=\frac{303}{5}=60.6$.

Answer:

$x = \frac{303}{5}$ (or $x = 60.6$)