Enter your answer and show all the steps that you use to solve this problem in the space provided.
Evaluate the expression for the given value of the variable.
|−4b−8|+∣∣−1−b2∣∣+2b3
; b=−2
To evaluate the expression |−4b−8|+∣∣−1−b^2∣∣+2b^3 when b=-2, we substitute -2 for b in the expression and simplify.
|−4(-2)−8|+∣∣−1−(-2)^2∣∣+2(-2)^3
=|8-8|+∣∣−1-4∣∣+2(-8)
=|0|+∣∣−5∣∣-16
=0+5-16
=5-16
=-11
Therefore, the value of the expression when b=-2 is -11.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the equation. Check for extraneous solutions.
9|9−8x|=2x+3
To solve the equation 9|9−8x|=2x+3, we need to isolate the variable x.
First, we can remove the absolute value by considering two cases: one where the expression inside the absolute value is positive and the other where it is negative.
Case 1: 9-8x > 0
Solving this inequality for x, we have:
9 - 8x > 0
-8x > -9
Dividing both sides by -8 and flipping the inequality sign since we are dividing by a negative number, we get:
x < 9/8
Case 2: 9-8x < 0
Solving this inequality for x, we have:
9 - 8x < 0
-8x < -9
Dividing both sides by -8 and flipping the inequality sign, we get:
x > 9/8
Now, we can check these solutions by substituting them back into the original equation and seeing if the equation holds true.
Checking x < 9/8:
9|9−8(9/8)| = 2(9/8) + 3
9|9 - 9| = 18/8 + 3
9(0) = 9/4 + 3
0 ≠ 21/4
Checking x > 9/8:
9|9−8(9/8)| = 2(9/8) + 3
9|9 - 9| = 18/8 + 3
9(0) = 9/4 + 3
0 ≠ 21/4
It is clear that neither of the solutions x < 9/8 or x > 9/8 satisfy the original equation.
Therefore, there are no solutions to the equation 9|9−8x|=2x+3, and there are no extraneous solutions to check.
To evaluate the expression |−4b−8|+∣∣−1−b2∣∣+2b3 when b is equal to -2, follow these steps:
Step 1: Substitute -2 for b in the expression.
|−4(-2)−8|+∣∣−1−(-2)^2∣∣+2(-2)^3
Step 2: Simplify the expression inside each absolute value symbol.
|8-8|+∣∣−1-4∣∣+2(-2)^3
|0|+∣∣−5∣∣+2(-2)^3
0+5+2(-2)^3
Step 3: Evaluate any exponents.
0+5+2(-8)
0+5-16
Step 4: Perform addition and subtraction in order from left to right.
5-16
Step 5: Finally, calculate the result.
-11