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http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w09_qp_31.pdf
Why is the answer to Q1 only one value? Why isn't it -1/2<x<5/4? And do question Q2 as well please! Thanks.
Q1 It's because you don't have a modulus on both sides of the inequality. When such is the case, you need to check your answer and see if it satisfies the inequality. So, here take any value of x which is greater than 5/4 eg x=2. Even though this value is outside the range, it satisfies the inequality. Hence you ans is only x> -1/2
Q2 3^(x+2) = 3^x + 3^2
(3^x)(3^2) = 3^x + 3^2
Take u=3^x
You get:
(3^2)u = u + 9
9u = u+9
u= 9/8
Now 3^x=9/8
x=0.107