Question

Can you guys help me with this question. -4(2x-7)<10-2x Write the solution in the form x ? A, where ? Represents the correct inequality symbol and a represents the value of the solution.

Answer 1

Answer:

x > 3

Step-by-step explanation:

You have the following inequality:

$-4(2x-7)<10-2x$

In order to obtain the solution for x, you first apply distribution property in the left term of the inequality:

$-4(2x)-4(-7)<10-2x\\\\-8x+28<10-2x$

Next, you sum 2x on both sides, and you subtract 28 on both sides too:

$-8x+2x+28-28<10-28-2x+2x\\\\-6x<-18$

(where you have simplifies similar terms)

Finally, you divide the inequality for -6, but you take into account that the inequality symbol change (because the operation with a negative term):

$\frac{-6x}{-6}<\frac{-18}{-6}\\\\x>3$

hence, the solution to the inequality is x > 3