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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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−
2
x
2
+
8
x
+
54
x
2
+
x
−
12
+
3
=
x
2
+
11
x
+
18
x
2
+
x
−
12
.
\frac{ - 2 x^2 + 8 x + 54 }{ x^2 + x - 12 } + 3=\frac{ x^2 + 11 x + 18 }{ x^2 + x - 12 }.
x
2
+
x
−
12
−
2
x
2
+
8
x
+
54
+
3
=
x
2
+
x
−
12
x
2
+
11
x
+
18
.
Hence, without using a calculator, solve the inequality
−
2
x
2
+
8
x
+
54
x
2
+
x
−
12
<
−
3
\frac{ - 2 x^2 + 8 x + 54 }{ x^2 + x - 12 } < -3
x
2
+
x
−
12
−
2
x
2
+
8
x
+
54
<
−
3
[5]
Answer
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