2019 H2 Mathematics Paper 1 Question 4

Equations and Inequalities

Answers

[2,4]{\left[ 2, 4 \right]}

Full solutions

(i)

(ii)

We add the graph of y=6{y=6} into our sketch
At intersection between the two graphs,
2x10=62x10=6\begin{align} && \quad 2^x - 10 &= 6 \\ && \quad 2^x - 10 &= -6 \\ \end{align}
From (1),{(1),}
2x=16x=4\begin{align*} 2^x &= 16 \\ x &= 4 \end{align*}
From (2),{(2),}
2x=4x=2\begin{align*} 2^x &= 4 \\ x &= 2 \end{align*}
From the graphs, interval for which 2x106:{|2^x - 10| \leq 6:}
[2,4]  \left[ 2, 4 \right] \; \blacksquare