Is the equation true, false, or open?
7m+10=3m+26
(1 point)
Responses
Open
Open
True
True
False
False
To determine if the equation is true, false, or open, we need to solve it to find the value of 'm'.
First, let's simplify the equation by combining like terms:
7m + 10 = 3m + 26
Now, let's isolate the variable 'm' by subtracting 3m from both sides:
7m - 3m + 10 = 3m - 3m + 26
4m + 10 = 26
Next, let's isolate 'm' by subtracting 10 from both sides:
4m + 10 - 10 = 26 - 10
4m = 16
To solve for 'm', we will divide both sides of the equation by 4:
(4m)/4 = 16/4
m = 4
Since we were able to find a unique value for 'm', the equation is true.
To determine if the equation 7m+10=3m+26 is true, false, or open, we need to solve the equation and see if it holds true for all values of m.
First, we can simplify the equation by combining like terms:
7m + 10 = 3m + 26
Next, we can isolate the variable m on one side of the equation by subtracting 3m from both sides:
7m - 3m + 10 = 26
Simplifying further, we get:
4m + 10 = 26
To solve for m, we can subtract 10 from both sides to isolate the term with m:
4m = 16
Finally, we divide both sides of the equation by 4 to solve for m:
m = 4
Now that we have solved the equation, we can substitute the value of m back into the original equation:
7(4) + 10 = 3(4) + 26
28 + 10 = 12 + 26
38 = 38
Since both sides of the equation are equal, the equation 7m+10=3m+26 is true for the value of m=4. Therefore, the correct response is "True".