The process of solving the equation exercise and the answer is 0.5 + 0.4 X

The process of solving the equation exercise and the answer is 0.5 + 0.4 X

One third of X is equal to 0.5 plus one fourth of X
4x=6+3x
4x-3x=6
x=6

To solve the system of equations x plus y equals one minus x minus three y equals five plus three X

(1)x+y=1-x
(2)x-3y=5+3x
From (1) we get 2x + y = 1
From (2), we get 2x + 3Y = - 5
The two formulas subtract x, 2Y = - 6, y = - 3
So x = 2
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The solution of equation x (2x-1) = - 3x (x + 1) + 5x ^ 2 + 3 is

6X ^ 2 + 4x-3x-2 = x ^ 2 + x-5x-5 + 5x ^ 2-10x is reduced to 6x ^ 2 + X-2 = 6x ^ 2-14x-5 15x = - 3x = - 1 / 5, and my steps are detailed,

X-3x-11 = 0, 3x-1 = 2x-5x, sum and product of two equations
It is known that the two parts of the equation 3x-x-1 = 0 are α and β respectively. Find α + β and 1 / A + 1 / b

(1)x^2-3x-1＝(x-α)(x-β)
→x^2-3x-1＝x^2-(α+β)x+αβ.
Compare the coefficients on both sides
α+β＝3,αβ＝-1.
(2)3x^2-1＝2x^2-5x
→x^2+5x-1＝0.
According to Vader's theorem:
α+β＝-5,αβ＝-1.
①α^2+β^2
＝(α+β)^2-αβ
＝25+1
＝26.
②1/α+1/β
＝(α+β)/αβ
＝(-5)/(-1)
＝5.

On increasing roots, the equation 2m + (x-m) / (x-1) = 0 has increasing roots, then M =?
The answers given in the book are m = - 1 and - 1 / 2. It's easy to understand when m = - 1. Why is m = - 1 / 2? Thank you
It should be wrong to write (2m + 1) / (x). Excuse me?

Here, we should not only consider the significance of denominator, but also pay attention to the problem of whether there is a solution to the equation. Since 1 is an increasing root, multiply both sides of the equation by X-1 at the same time to get 2m (x-1) + X + M = 0. Bring x = 1 into the solution to get the value of m as - 1. Consider the case that the increasing root is not 1, that is, the denominator itself is meaningful. At this time, multiply both sides by X-1 at the same time to get the equation, and change the left side of the equation to (2m + 1) x = M, Because the equation may have increasing roots because of no solution, the condition of no solution is 2m + 1 = 0, so the case of M = - 1 / 2 appears

2.6x + 3.2X = 11,6

2.6x x x 3.2X = 11.6
5.8x=11.6
x=11.6/5.8
x=2

3.6x minus 3.2X is equal to the solution of 144 equation

3.6x-3.2x=114
0.4x=114
x=285

It is known that one root of the equation 2x ^ 2-6x + 3P = 0 about X is - 1 / 2. Try to find another root and the value of P

Weida theorem
x1+x2=-b/a
-1/2+x2=3
x2=2.5
x1x2=c/a=p
p=-1.25

When Mingming solved the equation 2x-1 = x + A and then subtracted 1 to get the denominator, THE-1 on the right side of the equation was not multiplied by 3 to get the equation
The solution of the equation is x = 2

a=2,x=0

When Xiao Wang solves the equation, 2x of 3 minus 1 equals x of 3 plus a minus 1, and the denominator is removed, the - 1 on the right side of the equation is not multiplied by 3, so the solution of the equation is x equal to 2. Try to find the value of a and solve the equation

3 / 2x - 1 = 3 / x + A-1 3 / 2x = 3 / x + a substitute x = 2 into 3 / 2x = 3 / x + A to get 4 / 3 = 3 / 2 + a 3 / 2 = A and then substitute a