Is the inequality sometimes always never true-2(2x+9)>-4 x 9
I'll be glad to check your answer.
true
To determine whether the inequality -2(2x+9) > -4 x 9 is sometimes true, always true, or never true, we need to simplify the expression and compare the resulting inequality.
First, let's simplify the expression:
-2(2x+9) > -4 x 9
Start by applying the distributive property:
-4x - 18 > -36
Next, let's isolate the variable "x" by moving the constant terms to the other side of the inequality:
-4x > -36 + 18
-4x > -18
We have simplified the inequality to -4x > -18. Now, to determine if it is sometimes, always, or never true, we need to solve this inequality for "x".
When dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign is reversed. To maintain the direction, we will divide both sides by -4, but remember to flip the inequality sign:
x < -18 / -4
x < 4.5
The result is x < 4.5. This indicates that the inequality is sometimes true, depending on the values of x. Therefore, for any value of x that is less than 4.5, the inequality -2(2x+9) > -4 x 9 will be true.