# Modulus Assignment 1

Question 1.

1.

Find x such that $\vert x-2 \vert \geq 4$

Question 2.

2.

Find x such that $\vert \vert x-2 \vert – 1\vert \geq 3$

Question 3.

3.

Find x such that $\cfrac{\vert x+3 \vert + x}{x+2} \gt 1$

Question 4.

4.

Find x such that $\cfrac{x^2 -7\vert x\vert + 10}{x^2-6x+9} \lt 0$

Question 5.

5.

Find x such that $\left \lvert \cfrac{x^2 -5x + 4}{x^2-4} \right \rvert\leq 1$

Question 6.

6.

Find x such that $\vert x^2 +6x + 6\vert$   $=\vert x^2+4x+9\vert + \vert 2x-3 \vert$

Question 7.

7.

Find x such that $\vert x^2 +3x\vert \gt 2 – x^2$

Question 8.

8.

Solve the two equations simultaneously $\vert x^2 – 4x \vert \lt 5$  and  $\vert x+1 \vert \lt 3$

Question 9.

9.

Find x such that $\vert x^2 +x\vert \gt \vert x^2 + 5x -8 \vert$

Question 10.

10.

Find x such that $\vert x \vert +\left \lvert \cfrac{x}{x-1} \right \rvert = \cfrac{x^2}{\vert x – 1 \vert}$