問題
次の不等式を解け.
解説
- (1) $\dfrac14(x-7)<\dfrac13(2x+1)$
- $3(x-7)<4(2x+1)\ \Rightarrow\ 3x-21<8x+4\ \Rightarrow\ -5x<25\ \Rightarrow$$x>-5$
- (2) $2x-1\ge\dfrac{x+1}{3}$
- $6x-3\ge x+1\ \Rightarrow\ 5x\ge 4\ \Rightarrow$$x\ge \dfrac{4}{5}$
- (3) $\dfrac{x}{3}-\dfrac{x-5}{2}>0$
- $2x-3(x-5)>0\ \Rightarrow\ -x+15>0\ \Rightarrow$$x<15$
- (5) $-0.3x-1.5\le 0.2x-1.5$
- $-0.3x\le 0.2x\ \Rightarrow\ -0.5x\le 0\ \Rightarrow$$x\ge 0$
- (6) $0.4x-0.7\ge -1+\dfrac{x}{2}$
- $0.4x-\dfrac12x\ge -0.3\ \Rightarrow\ -0.1x\ge -0.3\ \Rightarrow$$x\le 3$
