Question

1/2 + 4m = 3m - 5/2

How do you solve for m

Answer 1

(1)/(2)+4m=3m-(5)/(2)

Reorder the polynomial (1)/(2)+4m alphabetically from left to right, starting with the highest order term.
4m+(1)/(2)=3m-(5)/(2)

Since 3m contains the variable to solve for, move it to the left-hand side of the equation by subtracting 3m from both sides.
4m+(1)/(2)-3m=-(5)/(2)

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, m is a factor of both 4m and -3m.
(4-3)m+(1)/(2)=-(5)/(2)

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of 4 and -3 and give the result the same sign as the integer with the greater absolute value.
(1)m+(1)/(2)=-(5)/(2)

Remove the parentheses.
m+(1)/(2)=-(5)/(2)

Since (1)/(2) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (1)/(2) from both sides.
m=-(1)/(2)-(5)/(2)

Combine the numerators of all fractions that have common denominators.
m=(-1-5)/(2)

Subtract 5 from -1 to get -6.
m=(-6)/(2)

Move the minus sign from the numerator to the front of the expression.
m=-(6)/(2)

Cancel the common factor of 2 in -(6)/(2).
m=-(^(3)<X>6<x>)/(<X>2<x>)

Remove the common factors that were cancelled out.
m=-3