SOLVE FOR THE VARIABLE
9/2m - 6 = -3 1/2 + 4m
nine halves m minus 6 = negative 3 and a half + 4m
thank you
Move every term with m in it onto one side, and the constants on the other. Divide the constant by the coefficient of m to get m.
9/2m - 4m = -3.5 + 6
2.5/0.5=5
M=5
9m/2 - 6 = -7/2 + 4m.
Multiply both sides by 2:
9m - 12 = -7 + 8m.
9m - 8m = 12 - 7.
m = 5.
To solve for the variable "m" in the equation:
9/2m - 6 = -3 1/2 + 4m
First, let's simplify the equation by converting all mixed fractions into improper fractions:
9/2m - 6 = -7/2 + 4m
Next, let's remove the fractions by multiplying every term in the equation by the least common denominator (LCD) of 2m:
(2m)(9/2m) - (2m)(6) = (2m)(-7/2) + (2m)(4m)
Simplifying, we get:
9 - 12m = -7m + 8m^2
Rearranging the terms, we get:
8m^2 + 12m - 7 = 0
This is now a quadratic equation. To solve it, we can either use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
m = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 8, b = 12, and c = -7. Substituting these values into the formula, we have:
m = (-12 ± √(12^2 - 4(8)(-7))) / (2(8))
Simplifying further:
m = (-12 ± √(144 + 224)) / 16
m = (-12 ± √368) / 16
m can be approximately equal to:
m ≈ (-12 ± 19.17) / 16
Now, we can calculate the two possible values of m:
m ≈ (-12 + 19.17) / 16 ≈ 7.17 / 16 ≈ 0.448
m ≈ (-12 - 19.17) / 16 ≈ -31.17 / 16 ≈ -1.946
Therefore, the possible solutions for m are approximately 0.448 and -1.946.