Question

Solve the system of inequalities:

2x-1 < x+3
5x−1 > 6−2x
x−5 < 0

Answer 1

`4 > x`

`1 < x`

`5 > x`

Explanation:

2x - 1 < x + 3

-2x - 2x

__________

−1 < −x + 3

-3 - 3

________

−4 < −x

`4 > x`

5x - 1 > 6 - 2x

-5x - 5x

__________

−1 > 6 - 7x

-6 - 6

________

−7 > −7x

__ ___

−7 −7

`1 < x`

x - 5 < 0

+ 5 + 5

______

`x < 5`

* The above answers are written in reverse, which are the exact same results.

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Answer 2

x<4, x>1,x<5

Explanation:

2x-1< x+3

2x-x<3+1

x<4

5x-1>6-2x

5x+2x>6+1

7x>7

=x>1

x-5<0

x<0+5

x<5