Evaluate the expression for the given value of the variable. Show your work.
[-4b-8]+[-1-b^2]+2b^3;b=-2
Solve the equation. Check for extraneous solutions. 9[9-8x]=2x+3. Show your work.
I really need help with both of these problems.
If b = -2, then since
(-2)^2 = (-2)(-2) = +4
(-2)^3 = (-2)(-2)(-2) = -8
[-4b-8]+[-1-b^2]+2b^3
= [-4(-2)-8]+[-1-(-2)^2]+2(-2)^3
= [8-8]+[-1-4]+2(-8)
= 0-5-16
= -21
9[9-8x] = 2x+3
81-72x = 2x+3
78 = 74x
x = 78/74 = 39/37
Sure! Let's start with the first problem:
Evaluate the expression [-4b-8]+[-1-b^2]+2b^3 when b = -2.
Step 1: Substitute the value of b into the expression:
[-4(-2)-8]+[-1-(-2)^2]+2(-2)^3
Step 2: Simplify each term:
[8-8]+[-1-4]+2(-8)
0+[-5]+(-16)
0-5-16
-21
Therefore, when b = -2, the expression evaluates to -21.
Now let's move on to the second problem:
Solve the equation 9[9-8x]=2x+3.
Step 1: Distribute the 9 on the left side of the equation:
81 - 72x = 2x + 3
Step 2: Combine like terms:
72x + 2x = 81 - 3
74x = 78
Step 3: Divide both sides by 74 to isolate x:
x = 78 / 74
x = 1.054
Step 4: Check for extraneous solutions by substituting x = 1.054 back into the original equation:
9[9 - 8(1.054)] = 2(1.054) + 3
9[9 - 8.432] = 2.108 + 3
9[0.568] = 5.108
5.112 ≠ 5.108
Therefore, there are no extraneous solutions. The solution to the equation is x = 1.054.
Sure, I can help you with both of these problems. Let's start with the first one.
Problem 1:
Evaluate the expression [-4b-8]+[-1-b^2]+2b^3 with the value of b = -2.
To solve this problem, we substitute the given value of b into the expression and perform the necessary calculations.
Step 1: Substitute the value of b into the expression.
[-4(-2) - 8] + [-1 - (-2)^2] + 2(-2)^3
Step 2: Simplify the expression inside the brackets first.
[8 - 8] + [-1 - 4] + 2(-8)
Step 3: Perform the calculations within each bracket.
[0] + [-5] - 16
Step 4: Simplify the expression by adding the values.
0 - 5 - 16 = -21
So, the value of the expression [-4b-8]+[-1-b^2]+2b^3 with b = -2 is -21.
Now, let's move on to the second problem.
Problem 2:
Solve the equation 9[9-8x] = 2x + 3 and check for extraneous solutions.
To solve this equation, we need to isolate the variable x by performing the necessary operations.
Step 1: Distribute 9 to the terms inside the brackets.
81 - 72x = 2x + 3
Step 2: Simplify the equation by combining like terms.
-72x - 2x = 3 - 81
Step 3: Perform the calculations.
-74x = -78
Step 4: Divide both sides of the equation by -74 to isolate x.
x = -78 / -74
Step 5: Simplify the fraction.
x = 1.0541 (rounded to four decimal places)
So, the solution to the equation 9[9-8x] = 2x + 3 is x = 1.0541.
To check for extraneous solutions, substitute the found value of x back into the original equation and see if both sides of the equation match. If they do, then the solution is valid.