Solve the equation
3/8(x=8)+1/8x=-1/2(x-7)
1.4x-3.1=0.2(x-27.5)
3/8(x=8)+1/8x=-1/2(x-7)
multiply by 8
3/(x-8) + 1/x = 4(x-7)
multiply by x
3x/(x-8) + 1 = 4x(x-7)
multiply by (x-8)
3x + (x-8) = 4x(x-8)(x-7)
3 x + x - 8 = 4x(x^2 - 15 x + 56)
4 x - 8 = 4 x^3 - 60 x^2 + 224 x
4 x^3 - 60 x^2 + 220 x + 8 = 0
x^3 - 15 x^2 + 55 x + 2 = 0
Google for polynomial solver
The roots of the polynomial x3−15x2+55x+2 are:
x1=−0.03601
x2=6.52858
x3=8.50743
Thanks
To solve the equation 3/8(x+8) + 1/8x = -1/2(x-7), we can first simplify the expressions on both sides of the equation.
Step 1: Distribute 3/8 to (x+8):
(3/8) * (x+8) = (3/8) * x + (3/8) * 8
3/8 * x + 3/8 * 8 = 3/8 * x + 3
Simplifying this, we get:
3/8x + 3 = 3/8x + 3
Step 2: Distribute -1/2 to (x-7):
(-1/2) * (x-7) = (-1/2) * x + (-1/2) * (-7)
-1/2 * x - 1/2 * (-7) = -1/2 * x + 7/2
Simplifying this, we get:
-1/2x - 7/2 = -1/2x + 7/2
Step 3: Substitute the simplified expressions back into the equation:
3/8x + 3 = -1/2x + 7/2
Step 4: Get rid of fractions by multiplying every term by 8:
8(3/8x + 3) = 8(-1/2x + 7/2)
Simplifying this gives us:
3x + 24 = -4x + 28
Step 5: Move all the variable terms to one side and the constant terms to the other side:
3x + 4x = 28 - 24
Simplifying this gives us:
7x = 4
Step 6: Solve for x by dividing both sides of the equation by 7:
x = 4/7
Therefore, the solution to the equation 3/8(x+8) + 1/8x = -1/2(x-7) is x = 4/7.
To solve the equation (3/8)(x+8) + (1/8)x = (-1/2)(x-7), we can follow the steps below:
Step 1: Distribute the coefficients on the left side of the equation.
(3/8)(x+8) + (1/8)x = (-1/2)(x-7)
(3/8)x + 3 + (1/8)x = (-1/2)x + (7/2)
Step 2: Combine like terms on both sides of the equation.
(3/8)x + (1/8)x + (1/2)x = (7/2) - 3
(7/8)x + (1/2)x = (7/2) - (6/2)
(7/8)x + (1/2)x = 1/2
Step 3: Find a common denominator and add the fractions on the left side.
(7/8)x + (4/8)x = 1/2
(11/8)x = 1/2
Step 4: Multiply both sides of the equation by the reciprocal of (11/8) to isolate x.
x = (1/2) * (8/11)
x = 4/11
Therefore, the solution to the equation is x = 4/11.
And now, let's move on to the second equation "1.4x-3.1=0.2(x-27.5)."
To solve this equation, we can follow these steps:
Step 1: Distribute 0.2 to the terms inside the parentheses on the right side.
1.4x - 3.1 = 0.2x - 5.5
Step 2: Combine like terms on both sides of the equation.
1.4x - 0.2x = -5.5 + 3.1
1.2x = -2.4
Step 3: Divide both sides of the equation by 1.2 to isolate x.
x = -2.4 / 1.2
x = -2
Therefore, the solution to the equation is x = -2.