Question

Solve the following inequalities 7 x minus 5 / 8 x + 3 >4
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Answer 1

`x>(8)/(51)`

Explanation:

`7x-(5)/(8)x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-(5)/(8)x+3-3>4-3\\\mathrm{Simplify}\\7x-(5)/(8)x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x* \:8-(5)/(8)x* \:8>1* \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\(51x)/(51)>(8)/(51)\\\\x>(8)/(51)`

I hope it helps :)

Answer 2

`x> (8)/(51)`

Explanation:

`7x - (5)/(8) x + 3>4`

Bring constants to one side, simplify:

`(51)/(8) x>4 - 3 \\ (51)/(8) x>1 \\ x>1 / (51)/(8) \\ x>1 * (8)/(51) \\ x> (8)/(51)`

*Note that the inequality sign only changes when you divide the whole inequality by a negative number.