Exercises 5 (Inequalities)

Solve the following and illustrate the solution on the number line:

1. \(2x+7>23\)

2. \(\{x: 6x-4>x\}\)

3. \(\{x: 2-3x \leq 2x+3\}\)

4. \(4x^2-9<0\)

5. \(x^2+3x+2\leq 5(x+2)\)

6. \(6x+5\geq x-5\)

7. \(|4x-5|<1\)

8. \(|-x+3|>2\)

9. \((3x-2)\div(1+x)<1\)

10. \((x+3)(x-4)<0\)

Solutions: 1. \(x>8\); 2. \(x>4/5\); 3. \(x\geq-1/5\); 4. \(-3/2< x< 3/2\); 5. \(-2\leq x\leq4\); 6. \(x\geq-2\); 7. \(1<x<3/2\); 8. \(x<1\) or \(x>5\); 9. \(-1<x<3/2\); 10. \(-3<x<4\)