Algebra

Sketch on the same diagram the graphs of $y = |2x - 9|$ and $y = 4x - 5$.

Solve the inequality $|2x - 9| < 4x - 5$.

Sketch on the same diagram the graphs of $y = |2x - 9|$ and $y = 4x - 5$.

Solve the inequality $|2x - 9| < 4x - 5$.

Sketch on the same diagram the graphs of $y = |2x - 9|$ and $y = 4x - 5$.

Solve the inequality $|2x - 9| < 4x - 5$.

Solve the equation $|2x - 3| = |5x + 2|$.

Hence solve the equation $|2\sec\theta - 3| = |5\sec\theta + 2|$ for $\pi < \theta < 2\pi$. Give your answer correct to 3 significant figures.

Find the quotient when $p(x)$ is divided by $(x^2 + 3)$ and show that the remainder is $-11$.

Hence find the real roots of the equation $p(x) + 11 = 0$. Give your answers in exact form.

Solve the equation $|2x - 3| = |5x + 2|$.

Hence solve the equation $|2\sec\theta - 3| = |5\sec\theta + 2|$ for $\pi < \theta < 2\pi$. Give your answer correct to 3 significant figures.

Sketch the graph of $y = |3x - 7|$, stating the coordinates of the points where the graph meets the axes.

Hence find the set of values of the constant $k$ for which the equation $|3x - 7| = k(x - 4)$ has exactly two real roots.

Sketch on the same diagram the graphs of $y = |3x - 8|$ and $y = 5 - x$.

Solve the inequality $|3x - 8| < 5 - x$.

Hence determine the largest integer $N$ satisfying the inequality $|3e^{0.1N} - 8| < 5 - e^{0.1N}$.