Is the inequality sometimes always never true-2(2x+9)>-4 x+9
-2(2x+9)>-4x+9
-4x-18 > -4x+9
-18 > 9
what do you think?
To determine whether the inequality -2(2x+9) > -4x+9 is sometimes, always, or never true, we need to find the values of x that satisfy the inequality.
Let's simplify the inequality step by step:
First, distribute -2 to the terms inside the parentheses:
-2(2x+9) > -4x+9
-4x - 18 > -4x + 9
Next, combine like terms by adding 4x to both sides of the inequality:
-4x - 4x - 18 > -4x + 4x + 9
-8x - 18 > 9
Now, add 18 to both sides:
-8x - 18 + 18 > 9 + 18
-8x > 27
Finally, divide both sides of the inequality by -8. Since we are dividing by a negative number, we need to reverse the inequality sign:
-8x / -8 < 27 / -8
x < -27/8
Therefore, the inequality -2(2x+9) > -4x+9 is sometimes true when x is less than -27/8.