Use the five-step strategy for solving word problems to find the number or numbers described in the following
exercise.
-$y _ { 1 } = \frac { 1 } { x + 7 } , y _ { 2 } = \frac { 1 } { x + 4 } , y _ { 3 } = \frac { - 3 } { x ^ { 2 } + 11 x + 28 }$, and the sum of $y _ { 1 }$ and 3 times $y _ { 2 }$ is $y _ { 3 }$.
A) $\{ 0 \}$
B) $\{ - 7 \}$
C) $\{ 4 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

Given $y_1 + 3y_2 = y_3$, substituting the expressions for $y_1$, $y_2$, and $y_3$ gives $\frac{1}{x+7} + \frac{3}{x+4} = \frac{-3}{x^2 + 11x + 28}$. Simplifying the equation does not yield a real solution for $x$ that satisfies all original expressions simultaneously, indicating that there is no solution, hence the correct answer is $\varnothing$.

Use the Five-Step Strategy for Solving Word Problems to Find y1=1x+7,y2=1x+4,y3=−3x2+11x+28y _ { 1 } = \frac { 1 } { x + 7 } , y _ { 2 } = \frac { 1 } { x + 4 } , y _ { 3 } = \frac { - 3 } { x ^ { 2 } + 11 x + 28 }y1​=x+71​,y2​=x+41​,y3​=x2+11x+28−3​

Use the Five-Step Strategy for Solving Word Problems to Find $y _ { 1 } = \frac { 1 } { x + 7 } , y _ { 2 } = \frac { 1 } { x + 4 } , y _ { 3 } = \frac { - 3 } { x ^ { 2 } + 11 x + 28 }$