Hi there!
We are given the inequality [tex]-2x + 3 \ \textgreater \ 3(2x - 1)[/tex] 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.
[tex]-2x + 3 \ \textgreater \ 3(2x - 1)[/tex]
-Distributive Property
[tex]-2x + 3 \ \textgreater \ 6x -3[/tex]
-Add 3 to both sides
[tex]-2x +6\ \textgreater \ 6x[/tex]
-Add 2x to both sides
[tex]6\ \textgreater \ 8x[/tex]
-Divide both sides by 8
[tex] \frac{6}{8} \ \textgreater \ x[/tex]
-Finally, simplify the fraction and rearrange the whole inequality so that x is starting
[tex]x\ \textless \ \frac{3}{4} [/tex]
Therefore, the solution to the inequality is [tex]x\ \textless \ \frac{3}{4}[/tex], 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!
