Question

1. \\(\frac{7}{11}=\frac{18}{x + 1}\\)\
2. \\(\frac{17}{15}=\frac{10}{2x - 2}\\)\
3. \\(\frac{6}{19}=\frac{x - 12}{2x - 2}\\)

Explanation:

Problem 15:

Step1: Cross-multiply to eliminate fractions

$7(x+1) = 18 \times 11$

Step2: Calculate right-hand side

$7(x+1) = 198$

Step3: Isolate the bracket term

$x+1 = \frac{198}{7}$

Step4: Solve for x

$x = \frac{198}{7} - 1 = \frac{198-7}{7} = \frac{191}{7}$

Problem 17:

Step1: Cross-multiply to eliminate fractions

$17(2x-2) = 10 \times 15$

Step2: Calculate right-hand side

$17(2x-2) = 150$

Step3: Isolate the bracket term

$2x-2 = \frac{150}{17}$

Step4: Simplify and solve for x

$2x = \frac{150}{17} + 2 = \frac{150+34}{17} = \frac{184}{17}$
$x = \frac{92}{17}$

Problem 19:

Step1: Cross-multiply to eliminate fractions

$6(2x-2) = 19(x-12)$

Step2: Expand both sides

$12x - 12 = 19x - 228$

Step3: Rearrange terms to isolate x

$-12 + 228 = 19x - 12x$

Step4: Solve for x

$216 = 7x$
$x = \frac{216}{7}$

Answer:

1. $x=\frac{191}{7}$
2. $x=\frac{92}{17}$
3. $x=\frac{216}{7}$