Question

Solve the inequality. Using a verbal statement, in simplest terms, describe the solution of the inequality. Be sure to include the terms, "greater than", "greater than or equal to", "less than", or "less than or equal to". HELP! Stuck on this last question

-2x + 3 > 3(2x - 1)

Answer 1

Hi there!
We are given the inequality
`-2x + 3 \ \textgreater \ 3(2x - 1)` and are told to solve it for x. However, we are also told to explain our solution using a verbal statement. First, let's solve the given inequality for x.

`-2x + 3 \ \textgreater \ 3(2x - 1)`
-Distributive Property

`-2x + 3 \ \textgreater \ 6x -3`
-Add 3 to both sides

`-2x +6\ \textgreater \ 6x`
-Add 2x to both sides

`6\ \textgreater \ 8x`
-Divide both sides by 8

`(6)/(8) \ \textgreater \ x`
-Finally, simplify the fraction and rearrange the whole inequality so that x is starting

`x\ \textless \ (3)/(4)`
Therefore, the solution to the inequality is
`x\ \textless \ (3)/(4)`, and the verbal statement is - 'x is any number less than 3/4, or 0.75.' Hope this answer has come of aid to you and have a great day!