Assignments

This series of exercises is about solving first-degree inequalities. An important aspect is that the inequality sign changes directions when both members of the inequality are divided or multiplied by a negative number: then a greater-than sign becomes a smaller-than sign and vice versa.

1. Solve:

$4x-6\leq2x-10$

2. Solve:

$2x-3(2x+6)>-2x+10$

3. Solve:

$3x(2x+4)-(x+3)<4x^2+2(x^2-2)$

4. Solve:

$2(2x-1)\geq3(x+2)+x$

5. Solve:

$2x+5+2(2x+1)<3(x-1)+3x+10$

6. Solve:

$-4x^2-7x+2x(2x-5)<-17$

7. Solve:

$2(2x-1)-4<3(x-2)+2(x+2)$

8. For which value(s) of $p$ does the following inequality have no solution:

$p(x-2)+3<-(x+p)$

9. Solve:

$3(x-1)+2x(x-3)\leq{x(x+1)+x(x-1)}$

10. Solve:

$\displaystyle\frac{x+1}{x-1}>0$

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