How do I solve x/4 - 3x/2 = -1/2?

x/4 - 3x/2 = -1/2
4(x/4 - 3x/2) = 4(-1/2)
x - 2(3x) = 2(-1)
x - 6x = -2
-5x = -2
x = -2/-5
x = 2/5 (0.4)

exchange of variable y = x^2 The equation turns into y^2 - 3y + 2 = 0 a quadratic; we use the quadratic formulation: y = [ +3 +/- sqrt( 9 - 8 )] / 2 y = [ 3 +/- a million ] / 2 utilising + y = (3 + a million)/2 = 4/2 = +2 in view that y = x^2, then x ^sqrt(y) = +/- sqrt(2) utilising - y = (3 - a million)/2 = 2/2 = a million x = sqrt(a million) = +/- a million 4 solutions (as envisioned from a 4th degree equation) --- it is likewise "legal" to wager the respond by potential of attempting diverse numbers, yet once you elect factors in a homework, you ought to instruct that your guesses are nicely concept out. For that, we use the Rational Root Theorem. It says that IF (a great if) there are rational suggestions, they are going to appear as if this p/q the place p and q are integers, and the place p is a divisor of the consistent term (the single with out variable, right here that's 2) q is a divisor of the main effective coefficient (the coefficient in front of the variable with the utmost degree, right here, that's the implicit a million in front of the x^4) the concept does not provide you the sign of the respond, so which you do ought to objective + and - one after the other. right here, p could be a million or 2 (the only divisors of two) q must be a million (the only divisor of a million); while q is a million, we are able to overlook approximately it. this supplies basically 4 "suspects" for the values p/q: +a million, -a million, +2, -2 you ought to objective all of them (one after the different) as a fee for x and, if the equation balances out, then it confirms the "suspect" as a valid answer. in this actual case, it happens that one and all suspects are responsible (that's somewhat uncommon -- in genuine existence, the Rational Root Theorem often supplies suspects that's necessary to launch).

x/4-3x/2= -1/2
4is the LCM of 4,2
so multiply x in first term by 1. since 4*1=4(LCM)
and multiply 3x in second term by 2. since 2*2=4(LCM)
nd write it as follows
(x-3x*2)/4= -1/2 here 4 is LCM
(x-6x)/4= -1/2
-5x/4= -1/2
multiply by -4 to both sides
5x= 4/2
5x=2
x=2/5

x.....3x.....-1
---- - ----- = ---- our LCD is 4 so we multiply and divide to the equation.
.4......2.......2

x-6x=-2 we combine like terms
-5x=-2 divide both sides by -5
x=2/5 answer//

Here is detailed step by step calculation.

x/4 - 3x/2 = -1/2
x-6x = -2 (multiply all by 4 to eliminate decimal )
-5x = -2
5x = 2 (Eliminate -ve)
x = 2/5 or 0.4 --Discover!!---

MUltiply through by 4

4(x/4) = x

3(3x/2) = 6x

4*(-1/2) = -2

x + 6x = -2

7x = -2

7x/7 = x = -2/7

(x / 4) - (3x / 2) = (-1 / 2)

Multiply both sides by the LCD 4 to get rid of the fractions.
4[(x / 4) - (3x / 2)] = 4(-1 / 2)
4(x / 4) - 4(3x / 2) = -2
1(x / 1) - 2(3x / 1) = -2
x - 6x = -2
-5x = -2

Divide both sides by -5.
-5x / -5 = -2 / -5
x = 2 / 5

ANSWER: x = 2 / 5

CHECK:

[(2 / 5) / 4] - [3(2 / 5) / 2] = (-1 / 2)?
(2 / 20) - [(6 / 5) / 2] = (-1 / 2)?
(1 / 10) - (6 / 10) = (-1 / 2)?
(-5 / 10) = (-1 / 2)?
(-1 / 2) = (-1 / 2)?
TRUE

First get rid of the denominators by multiplying everything by 4.

x/4 - 3x/2 = -1/2

x - 6x = -2
-5x = -2
5x = 2
x = 2/5

Multiply everything by 4 getting:
x -6x = -2
-5x = -2 = 2/5