From simple questions to complex issues, IDNLearn.com has the answers you need. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

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]