7[3m-(m+2)]>-6(m+3)
Use set-builder notation to describe the complete solution
{m|m > ? }
(type an equality symbol; then type an integer or a simplified fraction.)
7[3m-(m+2)] > -6(m+3).
Since the absolute value of a positive
number is = the absolute value of a negative number of the same magnitude,
we have 2 solutions.
+-7(3m-(m+2)) > -6(m+3),
+7(3m-m-2) > -6m-18,
7(2m-2) > -6m-18,
14m-14 > -6m-18,
14m + 6m > -18 + 14,
20m > -4,
m > -1/5.
-7(3m-(m+2)) > -6(m+3),
-7(3m-m-2) > -6m-18,
-7(2m-2) > -6m-18,
-14m + 14 > -6m-18,
-14m + 6m > -18-14,
-8m > -32,
m < 4.
Solution set: m > -1/5, and m < 4.
OR
-1/5 < m < 4.
To solve the inequality 7[3m-(m+2)]>-6(m+3), we need to simplify the expression and isolate the variable "m" on one side of the inequality.
First, let's simplify the expression inside the brackets:
7[3m-(m+2)] = 7[3m-m-2] = 7[2m-2] = 14m-14
Now, substitute this simplified expression back into the original inequality:
14m - 14 > -6(m+3)
Let's distribute -6 on the right side:
14m - 14 > -6m - 18
Next, let's gather all the "m" terms on the left side and the constants on the right side:
14m + 6m > -14 - 18
20m > -32
Now, divide both sides of the inequality by 20 to isolate the variable "m":
(20m)/20 > (-32)/20
m > -32/20
Simplifying further:
m > -8/5
Therefore, the solution to the inequality is:
{m | m > -8/5}