Question

solve the equation.\\(
\frac{25}{x + 1} = \frac{15}{4(x + 2)}
\\)\
step 1\
cross multiply.\
\\(\square \times \cdot 25 = (\square \times ) \cdot 15\\)\
simplify.\
\\(\square \times x + 200 = 15x + \square \times \\)

Explanation:

Step1: Cross multiply the equation

$4(x+2) \cdot 25 = (x+1) \cdot 15$

Step2: Expand both sides

$100(x+2) = 15(x+1)$
$100x + 200 = 15x + 15$

Step3: Isolate x terms

$100x - 15x = 15 - 200$
$85x = -185$

Step4: Solve for x

$x = \frac{-185}{85} = \frac{-37}{17}$

Answer:

$x = -\frac{37}{17}$

Filled-in blanks from the prompt:

Cross multiply: $\boldsymbol{4(x+2)} \cdot 25 = \boldsymbol{(x+1)} \cdot 15$
Simplify: $\boldsymbol{100}x + 200 = 15x + \boldsymbol{15}$