Solve linear inequality

4 You are given that \(a = \frac { 3 c + 2 a } { 2 c - 5 }\). Express \(a\) in terms of \(c\).

1 Solve the inequality \(2 ( x - 3 ) < 6 x + 15\).

2 Make \(r\) the subject of \(V = \frac { 4 } { 3 } \pi r ^ { 3 }\).

1 Solve the inequality \(2 x + 5 < 6 x - 3\).

3 Draw a number line to show the values of \(x\) which belong to the set \(\{ x : x \geqslant 2 \} \cap \{ x : x < 7 \}\).

1 Solve the inequality \(\frac { x } { 5 } > 6 - x\).

4. (a) Solve the inequality $$4 ( x - 2 ) < 2 x + 5$$ (b) Find the value of \(y\) such that $$4 ^ { y + 1 } = 8 ^ { 2 y - 1 } .$$

1 In this question you must show detailed reasoning. Andrea is comparing the prices charged by two different taxi firms.
Firm A charges \(\pounds 20\) for a 5 mile journey and \(\pounds 30\) for a 10 mile journey, and there is a linear relationship between the price and the length of the journey.
Firm B charges a pick-up fee of \(\pounds 3\) and then \(\pounds 2.40\) for each mile travelled.
Find the length of journey for which both firms would charge the same amount.

2 It is given that \(y = \frac { 1 } { x }\) and \(x < - 1\) Determine which statement below fully describes the possible values of \(y\).
Tick \(( \checkmark )\) one box.
[0pt] [1 mark] $$\begin{array} { l l } - \infty < y < - 1 & \square \\ y > - 1 & \square \\ - 1 < y < 0 & \square \\ y < 0 & \end{array}$$