Question

solve the equation. (\frac{25}{x + 1} = \frac{15}{4(x + 2)}) step 1 cross multiply. (4(x + 2) cdot 25 = left( \frac{x + 1}{x + 1}
ight) cdot 15) simplify. (100x + 200 = 15x + 15) step 2 subtract (15x + 200) from each side and simplify. (square) (x = -185) solve for (x). (x = square -185)

Explanation:

Step1: Cross multiply the equation

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

Step2: Simplify both sides

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

Step3: Isolate x terms

$$100x - 15x = 15 - 200$$

Step4: Simplify to solve for x

$$85x = -185$$
$$x = \frac{-185}{85} = -\frac{37}{17} \approx -2.18$$

Answer:

$x = -\frac{37}{17}$ (or $x \approx -2.18$)

Note: The pre-filled $x=-185$ in the image is incorrect; the correct value comes from properly simplifying after cross-multiplication.