2.7 Linear inequalities and absolute value inequalities  (Page 5/11)

When solving an inequality, explain what happened from Step 1 to Step 2:

$\begin{array}{ll}\text{Step 1}\hfill & -2x>6\hfill \\ \text{Step 2}\hfill & x<-3\hfill \end{array}$

When solving an inequality, we arrive at:

$\begin{array}{l}x+2<x+3\hfill \\ 2<3\hfill \end{array}$

Explain what our solution set is.

When writing our solution in interval notation, how do we represent all the real numbers?

When solving an inequality, we arrive at:

$\begin{array}{l}x+2>x+3\hfill \\ 2>3\hfill \end{array}$

Explain what our solution set is.

Describe how to graph $y=\left|x-3\right|$

$4x-7\le 9$

$3x+2\ge 7x-1$

$\mathrm{-2}x+3>x-5$

$4(x+3)\ge 2x-1$

$-\frac{1}{2}x\le \frac{-5}{4}+\frac{2}{5}x$

$\mathrm{-5}(x-1)+3>3x-4-4x$

$\mathrm{-3}(2x+1)>\mathrm{-2}(x+4)$

$\frac{x+3}{8}-\frac{x+5}{5}\ge \frac{3}{10}$

$\frac{x-1}{3}+\frac{x+2}{5}\le \frac{3}{5}$

$\left|x+9\right|\ge \mathrm{-6}$

$\left|2x+3\right|<7$

$|3x-1|>11$

$\left|2x+1\right|+1\le 6$

$\left|x-2\right|+4\ge 10$

$\left|\mathrm{-2}x+7\right|\le 13$

$|x-7|<\mathrm{-4}$

$|x-20|>\mathrm{-1}$

$\left|\frac{x-3}{4}\right|<2$

Distance of 5 units from the number 7

Distance of 3 units from the number 9

Distance of10 units from the number 4

Distance of 11 units from the number 1

$\mathrm{-4}<3x+2\le 18$

$3x+1>2x-5>x-7$

$3y<5-2y<7+y$

$2x-5<\mathrm{-11}\text{ or }5x+1\ge 6$

$x+7<x+2$

$|x-1|>2$

$\left|x+3\right|\ge 5$

$\left|x+7\right|\le 4$

$\left|x-2\right|<7$

$\left|x-2\right|<0$

$x+3<3x-4$

$x-2>2x+1$

$x+1>x+4$

$\frac{1}{2}x+1>\frac{1}{2}x-5$

$4x+1<\frac{1}{2}x+3$

$\{x|\mathrm{-1}<x<3\}$

$\{x|x\ge 7\}$

$\{x|x<4\}$

$\{x|x\text{ is all real numbers}\}$

$\left(-\infty ,6\right)$

$\left(4,+\infty \right)$

$[\mathrm{-3},5)$

$[\mathrm{-4},1]\cup [9,\infty )$