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19 P1 Q4
2019 H2 Mathematics Paper 1 Question 4
Equations and Inequalities
Answers
(i)
(ii)
[
2
,
4
]
{\left[ 2, 4 \right]}
[
2
,
4
]
Full solutions
(i)
(ii)
We add the graph of
y
=
6
{y=6}
y
=
6
into our sketch
At intersection between the two graphs,
2
x
−
10
=
6
2
x
−
10
=
−
6
\begin{align} && \quad 2^x - 10 &= 6 \\ && \quad 2^x - 10 &= -6 \\ \end{align}
2
x
−
10
2
x
−
10
=
6
=
−
6
From
(
1
)
,
{(1),}
(
1
)
,
2
x
=
16
x
=
4
\begin{align*} 2^x &= 16 \\ x &= 4 \end{align*}
2
x
x
=
16
=
4
From
(
2
)
,
{(2),}
(
2
)
,
2
x
=
4
x
=
2
\begin{align*} 2^x &= 4 \\ x &= 2 \end{align*}
2
x
x
=
4
=
2
From the graphs, interval for which
∣
2
x
−
10
∣
≤
6
:
{|2^x - 10| \leq 6:}
∣
2
x
−
10∣
≤
6
:
[
2
,
4
]
■
\left[ 2, 4 \right] \; \blacksquare
[
2
,
4
]
■
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