Inequalities (AQA A-Level Further Maths): Quizzes

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Inequalities
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What must you do when multiplying both sides of an inequality by a negative number?

Flip the inequality symbol

Solve 2x15<3+x\frac{2x-1}{-5} < 3 + x

x>2x > -2

If 3<2-3 < 2, what happens when you square both sides?

9>49 > 4 (inequality reverses)

Solve 18x135x321\frac{18x-135}{x-3} \leq 21. What is the solution?

x24x \leq -24 or x>3x > 3

For 18x135x3\frac{18x-135}{x-3}, what are the critical values used in sign chart analysis?

x=7.5x = 7.5 and x=3x = 3

For (x+3)(x+1)(x4)>0(x+3)(x+1)(x-4) > 0, what is the solution?

3<x<1-3 < x < -1 or x>4x > 4

For 5x+15x1<0\frac{5x+15}{x-1} < 0, what is the solution?

3<x<1-3 < x < 1

Solve x437x2+360x^4 - 37x^2 + 36 \geq 0. What is the solution?

x6x \leq -6 or 1x1-1 \leq x \leq 1 or x6x \geq 6

For real roots of x2(k+4)x+4=0x^2 - (k+4)x + 4 = 0, what condition must kk satisfy?

k0k \geq 0 or k8k \leq -8

Solve 04+x3x<10 \leq \frac{4+x}{3-x} < 1. What is the solution?

4x<12-4 \leq x < -\frac{1}{2}

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