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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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4
x
2
+
15
x
−
51
x
2
+
5
x
−
14
−
3
=
x
2
−
9
x
2
+
5
x
−
14
.
\frac{ 4 x^2 + 15 x - 51 }{ x^2 + 5 x - 14 } - 3=\frac{ x^2 - 9 }{ x^2 + 5 x - 14 }.
x
2
+
5
x
−
14
4
x
2
+
15
x
−
51
−
3
=
x
2
+
5
x
−
14
x
2
−
9
.
Hence, without using a calculator, solve the inequality
4
x
2
+
15
x
−
51
x
2
+
5
x
−
14
<
3
\frac{ 4 x^2 + 15 x - 51 }{ x^2 + 5 x - 14 } < 3
x
2
+
5
x
−
14
4
x
2
+
15
x
−
51
<
3
[5]
Answer
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