Problems from First degree inequations

Development:

We are going to solve 3 inequations step by step giving ,at the end, the values of $x$ for which the inequation is satisfied.

1. $2x-3<1\Rightarrow 2x<1+3\Rightarrow 2x<4\Rightarrow x<{\displaystyle \frac{4}{2}}\Rightarrow x<2$.

2. $x>3(x+1)\Rightarrow x>3x+3\Rightarrow x-3x>3\Rightarrow -2x>3\Rightarrow x>{\displaystyle \frac{3}{-2}}$.

3. $-{\displaystyle \frac{2}{3}}(3x-6)⩾2x-1\Rightarrow -{\displaystyle \frac{2}{3}}\cdot 3x+{\displaystyle \frac{2}{3}}\cdot 6⩾2x-1\Rightarrow$ $\Rightarrow -2x+4⩾2x-1\Rightarrow 4+1⩾2x+2x\Rightarrow 5⩾4x\Rightarrow {\displaystyle \frac{5}{4}}⩾x$.

Solution:

1. $x<2$

2. $x>{\displaystyle \frac{3}{-2}}$

3. $x⩽{\displaystyle \frac{5}{4}}$

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