Question

2-1/5(x-1)>2/3(2x+1) solve for x

Answer 1

`\large\boxed{x\leq1\to x\in(-\infty,\ 1]}`

Explanation:

`2-(1)/(5)(x-1)\geq(2)/(3)(2x+1)\qquad\text{multiply both sides by}\ LCM(5,\ 3)=15\\\\(15)(2)-15\!\!\!\!\!\diagup^3\cdot(1)/(5\!\!\!\!\!\diagup_1)(x-1)\geq15\!\!\!\!\!\diagup^5\cdot(2)/(3\!\!\!\!\!\diagup_1)(2x+1)\\\\30-3(x-1)\geq10(2x+1)\qquad\text{use the distributive property}\\\\30+(-3)(x)+(-3)(-1)\geq(10)(2x)+(10)(1)\\\\30-3x+3\geq20x+10\\\\33-3x\geq20x+10\qquad\text{subtract 33 from both sides}\\\\-3x\geq20x-23\qquad\text{subtract}\ 20x\ \text{from both sides}`

`-23x\geq-23\qquad\text{change the signs}\\\\23x\leq23\qquad\text{divide both sides by 23}\\\\x\leq1`