## Inequalities

Induction: Inequalities Go to the Forum to see more questions or ask your own Worked examples Show by induction that 3n ≥ 2n + 5 for n > 1. Show true for n = 2 LHS = 32 RHS = 2(2) + 5 = 9 [...]

20
07, 2017

Induction: Inequalities Go to the Forum to see more questions or ask your own Worked examples Show by induction that 3n ≥ 2n + 5 for n > 1. Show true for n = 2 LHS = 32 RHS = 2(2) + 5 = 9 [...]

22
03, 2017

Proving Inequalities worked examples Prove $$\left( {a + b} \right)\left( {\frac{1}{a} + \frac{1}{b}} \right) \ge 4$$ for a > 0 and b > 0. Consider (√a – √b)2 ≥ 0 since all square numbers are positive, it is a true statement to say that any perfect square will be larger than [...]

17
10, 2016

Sketching Inequalities when it is < or > the circles are 'open' or empty when it is ≤ or ≥ the circles are 'closed' or coloured in < and ≤ point to the left > and ≥ point to the right worked examples Solve 5x + 6 > x + 18 and sketch on the [...]

10
10, 2016

Inequalities Remember when dividing or multiplying by a negative to swap the sign. Remember when sketching inequalities: ◊ if it is ≤ or ≥ , then the circles must be filled ◊ if it is < or > , the the circles must be open worked examples further examples [...]

23
08, 2015

Equations with Like Terms worked examples When equations have like terms on the same side, we must first simplify where possible before solving the equation Solve 11p - 9p = 38. we see that on the left side of the equation we have like terms of p. Simplify 2p [...]

23
08, 2015

Inequalities worked examples Solve 5x + 6 > x + 18. 5x - x + 6 > x - x + 18 4x + 6 > 18 we need to gather the x's on one side (usually the left side) and the numbers on the right start by subtracting x from both [...]

19
08, 2015

Unknown Denominator Go to the Forum to see more questions or ask your own Worked examples Solve $$\frac1{7-3x}<1$$ and graph your solution on the number line. $$(7-3x)^2\times \frac{1}{7-3x}<1(7-3x)^2$$ multiply both sides by the denominator squared doing this avoids any issues with negative numbers and the direction of the inequality, as square [...]

19
08, 2015

Absolute Inequalities worked examples further examples harder examples Solve |4a + 3| + |3a - 7| >10 Case 1 4a + 3 + 3a - 7 = 10 7a - 4 = 10 7a = 14 a = [...]