Which property of equality justifies the step for solving the equation that is displayed?
3z/2 −5 = 10
3z/2 −5 + 5 = 10 + 5
3z/2=15
(1 point) Responses
Subtraction Property of Equality
Division Property of Equality
Multiplication Property of Equality
Addition Property of Equality
Addition Property of Equality
Using the properties of equality, find the solution to the equation 2f/5 − 8/5 +2f = 8.
(1 point) Responses
4
16/6
8/3
12
To solve the equation, we can simplify it first:
2f/5 − 8/5 + 2f = 8
To combine like terms, we can add the two "f" terms:
2f + 2f = 4f
Now, the equation becomes:
4f/5 − 8/5 = 8
To isolate the variable "f," we can multiply both sides of the equation by 5 to get rid of the denominator:
5 * (4f/5) − 5 * (8/5) = 5 * 8
This simplifies to:
4f − 8 = 40
Next, we can add 8 to both sides to move the constant term to the righthand side of the equation:
4f = 40 + 8
4f = 48
Finally, to solve for "f," we can divide both sides of the equation by 4:
f = 48/4
f = 12
Therefore, the solution to the equation is f = 12.
are you sure
Apologies for the confusion in my previous response. Let's go through the solution again:
2f/5 − 8/5 + 2f = 8
To combine the "f" terms, we have:
(2f + 2f)/5 − 8/5 = 8
Simplifying the numerator:
(4f)/5 − 8/5 = 8
Next, let's get rid of the denominator by multiplying both sides of the equation by 5:
5 * [(4f)/5] − 5 * (8/5) = 5 * 8
This simplifies to:
4f - 8 = 40
Now, we can add 8 to both sides of the equation to isolate the variable:
4f - 8 + 8 = 40 + 8
4f = 48
Lastly, we solve for "f" by dividing both sides of the equation by 4:
4f/4 = 48/4
f = 12
Therefore, the solution to the equation is f = 12.
How many solutions will the equation 2/3 (6m + 9) − 6 = 4m have?
(1 point) Responses
one solution
no solution
infinite/many
solutions two solutions
The equation 2/3(6m + 9) - 6 = 4m can be simplified as follows:
First, distribute 2/3 to (6m + 9):
(2/3) * 6m + (2/3) * 9 - 6 = 4m
This simplifies to:
4m + 6 - 6 = 4m
The term "-6" on both sides cancels out:
4m = 4m
Since the variable term is the same on both sides of the equation, this means that any value of "m" will satisfy the equation. In other words, there are infinitely many solutions for the equation.
Therefore, the answer is: infinite/many solutions.
Identify the pair of linear equations that have the same solution set.(1 point) Responses
4k − 5 = 2k and 8j − 2 = 3j
4 = k/2 + 5 and 4j−14/3 + 5 = 3
2 (3g + 5) − 2g = 2 (4 − g) and −36h/6 = 2
3 (m + 1) = 10 and 6n + 3 = 6 − n
The pair of linear equations that have the same solution set is:
3 (m + 1) = 10 and 6n + 3 = 6 − n
you're sure
Apologies for the incorrect response. Let's go through the options again:
1) 4k − 5 = 2k and 8j − 2 = 3j
2) 4 = k/2 + 5 and 4j−14/3 + 5 = 3
3) 2 (3g + 5) − 2g = 2 (4 − g) and −36h/6 = 2
4) 3 (m + 1) = 10 and 6n + 3 = 6 − n
To determine the pair of linear equations that have the same solution set, we need to look for two sets of equations that result in the same values for each variable.
From the options provided, the pair of equations that have the same solution set is:
4) 3 (m + 1) = 10 and 6n + 3 = 6 − n
This is because both equations have uniquely determined solutions for "m" and "n" respectively.
Tamara, Payton, Krish, and Haruki are analyzing the solution sets to the following linear equations. Tamara says that Equation A and Equation C have the same solution. Payton says Equation B and Equation C have the same solution. Krish says all three have the same solution. Haruki says that none of the equations have the same solution. Identify who is correct about the linear equations. Equation A: 3 (4 − 5h) − 7 = −12 + 2h
Equation B: 2 (p−3) − 1 =6p+14/2
Equation C: 2/3 v − 3 + 8/3 = −1
(1 point) Responses
Tamara
Krish
Payton
Haruki
To determine who is correct about the linear equations, let's analyze each equation:
Equation A: 3(4 − 5h) − 7 = −12 + 2h
Equation B: 2(p − 3) − 1 = 6p + 14/2
Equation C: (2/3)v − 3 + 8/3 = −1
To find out if any two equations have the same solution, we need to compare the coefficients and constants of each variable in the equations.
Comparing the variables in Equation A and Equation C, we have:
For "h": Equation A has -5h, while Equation C has no "h" term.
For "v": Equation C has (2/3)v, while Equation A has no "v" term.
Therefore, Equation A and Equation C do not have the same solution.
Comparing the variables in Equation B and Equation C, we have:
For "p": Equation B has p, while Equation C has no "p" term.
For "v": Equation C has (2/3)v, while Equation B has no "v" term.
Therefore, Equation B and Equation C do not have the same solution.
Comparing the variables in Equation A and Equation B, we have:
For "h": Equation A has -5h, while Equation B has no "h" term.
For "p": Equation B has p, while Equation A has no "p" term.
Therefore, Equation A and Equation B do not have the same solution.
Based on the analysis, Haruki is correct when he says that none of the equations have the same solution.