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