I would really appreciate it someone helped me with this information.
1. Solve the inequality: |3 - 3x/4| >= 9
Solve for x
2.(x - 2)(x + 1) = 4
and factor completely
64 + a^3
1. 3 - 3x/4 ≥ 9 OR -3 + 3x/4 ≥ 9
12 - 3x ≥ 36 OR -12 + 3x ≥ 36
-3x ≥ 24 OR 3x ≥ 48
x ≤ -8 or x ≥ 16
2. expand and rearrange to a quadratic
x^2 - x - 6 = 0
(x-3)(x+2) = 0
x = 3 or x = -2
3. You should know a formula for factoring the sum of cubes:
A^3 + B^3 = (A+B)(A^2 - AB + B^2)
notice that
64 + a^3
= 4^3 + a^3
take it from there.
Thank you. So can that be factored anymore?
and would I do this oen the same way?
7. 2x^4 + 16x
yes, I gave you the formula and the hint.
64 + a^3
= (4+a)(16 - 4a + a^2)
What about the other one?? the same way??
Thanks reiny for your help.
yes, take out a common factor of 2x first to get
2x(x^3 + 8) and recognize 8 as 2^3
Thanks
1. To solve the inequality |3 - 3x/4| >= 9, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 3 - 3x/4 ≥ 9
Simplify the inequality:
3 - 3x/4 ≥ 9
Multiply both sides by 4 to eliminate the fraction:
12 - 3x ≥ 36
Subtract 12 from both sides:
-3x ≥ 24
Divide both sides by -3, remembering to reverse the inequality sign when dividing by a negative number:
x ≤ -8
Case 2: - (3 - 3x/4) ≥ 9
Simplify the inequality:
-3 + 3x/4 ≥ 9
Multiply both sides by 4 to eliminate the fraction and distribute the negative sign:
-12 + 3x ≥ 36
Add 12 to both sides:
3x ≥ 48
Divide both sides by 3:
x ≥ 16
Combining the two cases, the solution to the inequality |3 - 3x/4| ≥ 9 is:
x ≤ -8 or x ≥ 16
2. To solve the equation (x - 2)(x + 1) = 4 and factor completely, follow these steps:
Expand the expression:
x(x + 1) - 2(x + 1) = 4
x^2 + x - 2x - 2 = 4
Simplify:
x^2 - x - 6 = 0
To factor the quadratic equation, find two numbers that multiply to -6 (the product of the coefficient of x^2 and the constant term) and add up to the coefficient of x (-1).
In this case, the numbers are -3 and 2:
(x - 3)(x + 2) = 0
So, the factored form of the equation is:
(x - 3)(x + 2) = 0
3. To simplify the expression 64 + a^3, there is no specific method to factor or simplify it further, as it is already in its simplest form. The expression remains as 64 + a^3.