4x + 5x + 12 = -6 (given)
9x + 12 = -6 (simplify)
9x = -18 (subtraction)
x = -2 (addition)
Which reason is incorrect?
Responses
A additionaddition
B givengiven
C simplifysimplify
D subtraction
bro i got it wrong
I apologize for the mistake. The reason that is incorrect is D - subtraction. The equation should be 9x = -18 after simplifying, and to solve for x, we need to divide both sides of the equation by 9, not subtract. Therefore, the correct reason should be division.
Step 1: 4x + 5 < 6x + 1 (Given)
Step 2: −2x + 5 < 1 (Subtraction)
Step 3: −2x < 6 (Addition)
Step 4: x > −3 (Division)
Mia is trying to find her mistake in the problem shown. In which step did she first make a mistake?
Responses
A Step 1Step 1
B Step 2Step 2
C Step 3Step 3
D Step 4
The correct answer would be D - Step 4.
are u sure
I apologize for the confusion. Upon reviewing the steps, I realize that my previous response was incorrect. The correct answer is actually B - Step 2. Mia made a mistake in subtracting 6x from both sides in Step 2.
How many solutions does this equation have?
2+6x2
= 3x + 3
The equation you provided doesn't seem to be formatted correctly. Could you please double-check or provide more information?
How many solutions does this equation have?
2+6x2= 3x + 3
To determine the number of solutions for the equation 2 + 6x^2 = 3x + 3, we need to simplify the equation and see if it has a unique solution, infinite solutions, or no solution.
First, let's simplify the equation:
2 + 6x^2 = 3x + 3
Rearranging the equation:
6x^2 - 3x = 3 - 2
6x^2 - 3x = 1
Dividing by 3:
2x^2 - x = 1/3
Now, we have a quadratic equation in standard form: 2x^2 - x - 1/3 = 0
Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), where a, b, c are coefficients of the quadratic equation, we can determine the solutions.
In this case, a = 2, b = -1, c = -1/3.
Plugging these values into the quadratic formula, we have:
x = (-(-1) ± √((-1)^2 - 4*2*(-1/3)))/(2*2)
x = (1 ± √(1 + 8/3))/(4)
x = (1 ± √(11/3))/(4)
Since the expression inside the square root (√(11/3)) is positive, we have two real solutions for x.
Therefore, the equation has 2 solutions.
Solving the equation 6x + 2(x − 1) = 30
Given: 6x + 2(x − 1) = 30
Step 1: 6x + 2x − 2 = 30
Step 2: 8x − 2 = 30
Step 3: 8x − 2 + 2 = 30 + 2
Step 4: 8x8
= 328
Step 5: x = 4
Question 1
Identify the property that justifies Step 1 when solving the given equation.
Responses
A Distributive PropertyDistributive Property
B Substitution PropertySubstitution Property
C Symmetric PropertySymmetric Property
D Multiplication PropertyMultiplication Property
Question 2
Identify the property that justifies Step 2 when solving the given equation.
Responses
A Reflexive PropertyReflexive Property
B Substitution PropertySubstitution Property
C Symmetric PropertySymmetric Property
D Multiplication PropertyMultiplication Property
Question 1: The property that justifies Step 1 is A - Distributive Property.
Question 2: The property that justifies Step 2 is B - Substitution Property.
Solve: 3(2x - 5) = 6x - 15
Responses
A 00
B 11
C 2020
D no solutionno solution
E infinitely many solutions
Let's solve the equation step by step:
3(2x - 5) = 6x - 15
Step 1: Distribute the 3 on the left side of the equation:
6x - 15 = 6x - 15
Step 2: Simplify both sides of the equation:
6x - 15 = 6x - 15
Step 3: Subtract 6x from both sides of the equation:
-15 = -15
Step 4: Subtract -15 from both sides of the equation:
0 = 0
The variable x has been eliminated from the equation, and we are left with a true statement: 0 = 0.
This means that the equation is an identity and holds true for all values of x. Therefore, the solution is E - infinitely many solutions.