Question

3/4(х+2) +2/5(х-1) =21/40 1/2(2-х) +3/4(х-1) =1/12 1/3(2х+1) +2(1-х) =3 1/3

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve this system of linear equations, we'll start by simplifying each equation and then solve for the value of 'x'. Here are the equations you've provided:

1. $\frac{3}{4}(x+2) + \frac{2}{5}(x-1) = \frac{21}{40}$
2. $\frac{1}{2}(2-x) + \frac{3}{4}(x-1) = \frac{1}{12}$
3. $\frac{1}{3}(2x+1) + 2(1-x) = \frac{1}{3}$

Let's solve these equations one by one.

Equation 1: $\frac{3}{4}(x+2) + \frac{2}{5}(x-1) = \frac{21}{40}$

First, clear the fractions by multiplying both sides by the least common multiple (LCM) of 4 and 5, which is 20.

$20 \cdot \left(\frac{3}{4}(x+2) + \frac{2}{5}(x-1)\right) = 20 \cdot \frac{21}{40}$

Simplify:

$15(x+2) + 8(x-1) = 21$

Now, distribute and simplify:

$15x + 30 + 8x - 8 = 21$

Combine like terms:

$23x + 22 = 21$

Subtract 22 from both sides:

$23x = -1$

Divide by 23:

$x = \frac{-1}{23}$

Equation 2: $\frac{1}{2}(2-x) + \frac{3/4}(x-1) = \frac{1}{12}$

Again, clear the fractions by multiplying both sides by the LCM of 2 and 4, which is 4.

$4 \cdot \left(\frac{1}{2}(2-x) + \frac{3}{4}(x-1)\right) = 4 \cdot \frac{1}{12}$

Simplify:

$2(2-x) + 3(x-1) = \frac{1}{3}$

Distribute and simplify:

$4 - 2x + 3x - 3 = \frac{1}{3}$

Combine like terms:

$x + 1 = \frac{1}{3}$

Subtract 1 from both sides:

$x = \frac{1}{3} - 1$

$x = \frac{1}{3} - \frac{3}{3} = -\frac{2}{3}$

Equation 3: $\frac{1}{3}(2x+1) + 2(1-x) = \frac{1}{3}$

Clear the fractions by multiplying both sides by the LCM of 3.

$3 \cdot \left(\frac{1}{3}(2x+1) + 2(1-x)\right) = 3 \cdot \frac{1}{3}$

Simplify:

$2(2x+1) + 6(1-x) = 1$