The diagram shows the graphs of $y=|a-bx|$ and $y=|mx-6|$, where $a$, $b$ and $m$ are

Question

The diagram shows the graphs of $y=|a-bx|$ and $y=|mx-6|$, where $a$, $b$ and $m$ are positive constants. The graph of $y=|a-bx|$ meets the $x$-axis at the point $\left(\dfrac94,0\right)$. The solution set of the inequality $|mx-6|<|a-bx|$ is given as $\{x:x\in\mathbb{R},\ x<1\text{ or}\hspace{0.5em}x>3\}$. Find the values of $a$, $b$ and $m$.[4] Given that $k$ is a constant and $k>1$, solve the inequality $\dfrac{kx^2+1}{x^2+(k+1)x+k}>-1$, giving your answer in terms of $k$. [4]

Accepted Answer

(a) $a=9,\ b=4,\ m=1$ (b) $x-1$

2025 ACJC Promo Q4

2025 ACJC Promo Q4

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