1st Question:
Substitute b=-2 into the expression |-4b-8| + |-1-b^2|+2b^3:
|-4(-2)-8| + |-1-(-2)^2|+2(-2)^3 = |8-8| + |-1-4| -16 = 0+5-16 = -11
Answer: -11
2nd Question:
First, we need to simplify the expression inside the absolute value:
9|9-8x| = 2x+3
|9-8x| = (2x+3)/9
Then, we have two cases:
1) 9-8x = (2x+3)/9
Multiplying both sides by 9, we have:
81 - 72x = 2x+3
Solving for x, we get:
74x = 78
x = 39/37
However, we need to check if this solution is extraneous by substituting it back into the original equation:
9|9-8(39/37)| = 2(39/37)+3
9|(315/37)| = (78/37)+3
2835/37 = 231/37
This is not true, so x = 39/37 is an extraneous solution and we discard it.
2) 9-8x = -(2x+3)/9
Multiplying both sides by 9, we have:
81 - 72x = -(2x+3)
Solving for x, we get:
x = -87/74
Again, we need to check if this solution is extraneous:
9|9-8(-87/74)| = 2(-87/74)+3
9|(903/37)| = (-171/37)
This is not true, so x = -87/74 is also an extraneous solution and we discard it.
Answer: There are no solutions to the equation 9|9-8x|=2x+3.
Hey I need help on the test Equations, Expressions, and inequalities unit test part two. Please show all the work! I really suck at math and would really appreciate the help.
1st Question-
Evaluate the expression for the given value of the variable.
|-4b-8| + |-1-b^2|+2b^3; b=-2
2nd Question -
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
1 answer