On the question below, Bob Pursley said it was correct, however, I just wanted to make sure that it's not supposed to have another x value since it has x^2 in it.
Solve the inequality:
(2x-3)(4x)+x^2=>(3x+4)^2
I did 2x-3*4x
9x^2-12x on the left side
on the right side:
9x^2+24x+16
I substracted everything on the right side over to the left and made it => zero
9x^2-12x-9x^2-24x-16=>0
-36x-16=>0
x=<4/-9
I'm not sure if this is right or if I made an error somewhere.
Math - bobpursley, Saturday, September 12, 2009 at 2:49pm
it is correct.
Math - muffy, Saturday, September 12, 2009 at 2:54pm
THANKS!
Figured it out -- sorry for doubting you. It's right!
To solve the inequality (2x-3)(4x)+x^2 ≥ (3x+4)^2, you correctly multiplied out the expressions on both sides to get:
9x^2-12x ≥ 9x^2+24x+16
Next, you subtracted everything on the right side over to the left side and made it equal to zero:
9x^2-12x-9x^2-24x-16 ≥ 0
However, in this step, it seems like you made a mistake when subtracting the terms.
The correct subtraction would be:
(9x^2 - 9x^2) + (-12x - 24x) - 16 ≥ 0
Simplifying further, we get:
-36x - 16 ≥ 0
To find the value of x, we need to solve this inequality.
To do that, let's isolate the variable x by adding 16 to both sides:
-36x ≥ 16
Then, divide both sides by -36.
Important: When dividing or multiplying both sides of an inequality by a negative number, we need to reverse the inequality symbol.
Dividing by -36 gives:
x ≤ 16/-36
Now, simplify the fraction:
x ≤ -4/9
So, the correct solution to the inequality is x ≤ -4/9.
In the original discussion, Bob Pursley confirmed that your answer was correct. It seems that the expression does not have any other x value, as you correctly determined.