Question

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

Answer 1

We will solve as follows:

`4(x-5)+10>2(5x-2)-4\Rightarrow4x-20+10>10x-4-4x`
`\Rightarrow4x-10>6x-4\Rightarrow-2x>6\Rightarrow x<-3`

So, the solution is x < -3.

***Breakdown:

*After we obtain:

`4x-10>6x-4`

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

`\Rightarrow4x-6x>-4+10\Rightarrow-2x>6`

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:

`\Rightarrow x<(6)/(-2)\Rightarrow x<-3`