Which property of equality justifies the step for solving the equation that is displayed? 3z2−5=10 3z2−5+5=10+5 3z2=15
Addition Property of Equality Addition Property of Equality Division Property of Equality Division Property of Equality Subtraction Property of Equality Subtraction Property of Equality Multiplication Property of Equality
Subtraction Property of Equality
Using the properties of equality, find the solution to the equation 2f/5−8/5+2f=8 .
8/3
16/6
12
4
To solve the equation 2f/5−8/5+2f=8, we can use the properties of equality to simplify and isolate the variable f.
First, let's simplify the left side of the equation:
2f/5−8/5+2f
= (2f + 2f - 8) / 5 [combining like terms]
Next, let's simplify the numerator:
2f + 2f - 8
= 4f - 8
Now, we have:
(4f - 8) / 5 = 8
To isolate the variable f, we can multiply both sides of the equation by 5:
5 * (4f - 8) / 5 = 8 * 5
4f - 8 = 40
Now, let's isolate f by adding 8 to both sides of the equation:
4f - 8 + 8 = 40 + 8
4f = 48
Finally, we divide both sides of the equation by 4 to find the value of f:
4f / 4 = 48 / 4
f = 12
Therefore, the solution to the equation 2f/5−8/5+2f=8 is f = 12.
are you sure?
Apologies for the mistake in the previous response. Let's re-evaluate the equation correctly.
The equation is 2f/5 − 8/5 + 2f = 8.
To solve this equation, we will simplify and isolate the variable f.
First, let's combine the like terms on the left side of the equation:
(2f + 2f)/5 − 8/5 = 8
(4f)/5 − 8/5 = 8
Next, let's isolate the term with f by subtracting 8/5 from both sides:
(4f)/5 = 8 + 8/5
(4f)/5 = (40 + 8)/5
(4f)/5 = 48/5
To eliminate the fraction, we can multiply both sides of the equation by 5:
5 * (4f)/5 = 5 * (48/5)
4f = 48
Finally, we divide both sides of the equation by 4 to find the value of f:
4f/4 = 48/4
f = 12
Therefore, the correct solution to the equation 2f/5 − 8/5 + 2f = 8 is f = 12.
How many solutions will the equation 2/3(6m+9)−6=4m have?
two solutions two solutions no solution no solution infinite/many solutions infinite/many solutions one solution one solution
The equation 2/3(6m+9)−6=4m can be simplified using the distributive property and then solving for m.
First, let's simplify the left side of the equation:
2/3(6m+9)−6
= (2/3)(6m) + (2/3)(9) − 6
= (4m) + (6/3) − 6
= 4m + 2 − 6
= 4m - 4
Now, the equation becomes:
4m - 4 = 4m
We can see that the variable m is on both sides of the equation. This means that when we solve for m, it will result in an identity equation, indicating that all values of m will satisfy the equation.
Therefore, the equation 2/3(6m+9)−6=4m has infinite/many solutions.
Identify the pair of linear equations that have the same solution set.
2(3g+5)−2g=2(4−g) and −36h6=2 2 left parenthesis 3 g plus 5 right parenthesis minus 2 g equals 2 left parenthesis 4 minus g right parenthesis and Start Fraction negative 36 h over 6 End Fraction equals 2 4k−5=2k and 8j−2=3j 4 k minus 5 equals 2 k and 8 j minus 2 equals 3 j 4=k2+5 and 4j−143+5=3 4 equals Start Fraction k over 2 End Fraction plus 5 and Start Fraction 4 j minus 14 over 3 End Fraction plus 5 equals 3 3(m+1)=10 and 6n+3=6−n
The pair of linear equations that have the same solution set is:
2(3g+5)−2g=2(4−g) and −36h6=2
In the first equation, we can simplify and solve for g:
6g+10 - 2g = 8 - 2g
4g + 10 = 8 - 2g
6g + 10 = 8
6g = -2
g = -1/3
In the second equation, we have:
-36h/6 = 2
-6h = 2
h = -1/3
Therefore, both equations have the same solution set with g = -1/3 and h = -1/3.