Put LP under the standard form if there is a variable which is not non negative

How we can put a linear program under the standard form if there is a variable which is negative and other variables are not negative?

x1∈Rx_1 \in\mathbb R, x2≥0x_2 \geq 0, x3≥0x_3 \geq 0

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Define x1=x3−x4x_1=x_3-x_4 where x3,x4x_3, x_4 are non-negative.
– Macavity
Oct 20 at 18:47

  

 

@Macavity But x3 is already defined. Could you answer with example please?
– Ramon
Oct 20 at 21:07

  

 

We can introduce variables x4 and x5: x4≥0, x5≥0 such that x1 = x4 – x5?
– Ramon
Oct 20 at 21:13

  

 

Yes. You can replace any unconstrained variable with the difference of two (new) non-negative variables to get a standard form LP.
– Macavity
Oct 21 at 1:46

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