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Solve the inequality. State the solution in inequality notation. 4(x - 5) + 10 > 2(5x – 2) – 4x

Sagot :

We will solve as follows:

[tex]4(x-5)+10>2(5x-2)-4\Rightarrow4x-20+10>10x-4-4x[/tex][tex]\Rightarrow4x-10>6x-4\Rightarrow-2x>6\Rightarrow x<-3[/tex]

So, the solution is x < -3.

***Breakdown:

*After we obtain:

[tex]4x-10>6x-4[/tex]

We operate like terms, that is we separate the variables and integers in the different side [Operating as if it were a normal equation]:

[tex]\Rightarrow4x-6x>-4+10\Rightarrow-2x>6[/tex]

After this, we know that by dividing and/or multiplying by negative values in the inequality the orientation of the inequality will shift [That is if it was "<" then it will become ">" and viceversa], that is:

[tex]\Rightarrow x<\frac{6}{-2}\Rightarrow x<-3[/tex]

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