Question #7d5d1b32 - SAT Suite Question Bank

ID: 7d5d1b32

Modded SAT Question Bank by Abdullah Mallik

$2 (k x - n) = - \frac{28}{15} x - \frac{36}{19}$

In the given equation, $k$ and $n$ are constants and $n greater than 1$ . The equation has no solution. What is the value of $k$ ?

Toggle Answer

Tip: Press CTRL/Command to toggle answer

Correct Answer: -.9333, -14/15

Rationale

The correct answer is $- \frac{14}{15}$ . A linear equation in the form $a x + b = c x + d$ has no solution only when the coefficients of $x$ on each side of the equation are equal and the constant terms are not equal. Dividing both sides of the given equation by $2$ yields $k x - n = - \frac{28}{30} x - \frac{36}{38}$ , or $k x - n = - \frac{14}{15} x - \frac{18}{19}$ . Since it’s given that the equation has no solution, the coefficient of $x$ on both sides of this equation must be equal, and the constant terms on both sides of this equation must not be equal. Since $StartFraction 18 Over 19 EndFraction less than 1$ , and it's given that $n greater than 1$ , the second condition is true. Thus, $k$ must be equal to $- \frac{14}{15}$ . Note that -14/15, -.9333, and -0.933 are examples of ways to enter a correct answer.

Question Difficulty: Hard