Question

Find the solution set for the following inequality 4x-7>6x-13

Answer 1

`\\\mathrm{Solution:}\:&\:x < 3\:\\\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:3\right)`

Explanation:

`\textrm{We have the inequality $4x-7 > 6x-13$}\\\\\\textrm{Move 7 to the right side: }\\4x + 7 - 7 > 6x -13 + 7\\\\4x > 6x -6\\\\`

`\mathrm{Move}\:6x\:\mathrm{to\:the\:left\:side}`

`4x-6x > 6x-6-6x`

`-2x > -6`

`\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}`

`\left(-2x\right)\left(-1\right) < \left(-6\right)\left(-1\right)`

`== > 2x < 6`

`\mathrm{Divide\:both\:sides\:by\:}2\\\\`

`\fdrac{2x}{2} < (6)/(2)\\\\x < 3`

So the solution set of the inequality is x < 3 which in interval notation is
(- ∞ , 3)