Question

1)108:90=42:5х 2)(7х-3)/4 = (5-2х)/6 3)5/2х = 3/(4-х) 5)2/(6-х)= 4/(5х+3)

Answer 1

1. 108:90=42:5х

1.2=$\frac{42}{5}$x

$\frac{5}{42}$*1.2=x

$\frac{5}{42}$*$\frac{6}{5}$=x

$\frac{1}{7}$=x

x=$\frac{1}{7}$

2.(7х-3)/4 = (5-2х)/6

6(7x-3)=4(5-2x)

42x-18=20-8x

42x+8x=20+18

50x=38

x=$\frac{19}{25}$

3. 5/2х = 3/(4-х)

$\frac{5}{2}$x=$\frac{3}{4-x}$, x$\neq$4

5x=$\frac{6}{4-x}$

5x*(4-x)=6

5x*(4-x)-6=0

20x-$5x^{2}$-6=0

-$5x^{2}$+20x-6=0

5x2-20x+6=0

x=$\frac{-(-20)+-\sqrt{(-20)^{2}-4*5*6 } )}{2*5}$

x=$\frac{20+-\sqrt{400-120} }{10}$

x=$\frac{20+-\sqrt{280} }{10}$

x=$\frac{20+-2\sqrt{70} }{10}$

x=$\frac{20+2\sqrt{70} }{10}$  x=$\frac{20-2\sqrt{70} }{10}$

x=$\frac{10+\sqrt{70} }{5}$  x=$\frac{10-\sqrt{70} }{5}$, x$\neq$4

x_{1} =$\frac{10-\sqrt{70} }{5}$ x_{2} =$\frac{10+\sqrt{70} }{5}$

5. 2/(6-х)= 4/(5х+3)

$\frac{2}{6-x} =\frac{4}{5x+3}$, x

Answer 2

To solve the given equations, we'll work through each one step-by-step:

1. 108:90 = 42:5x

Step 1: Simplify both sides of the equation 108/90 = 42/(5x)

Step 2: Cross-multiply 108 * 5x = 90 * 42

Step 3: Solve for x 540x = 3780

Step 4: Divide both sides by 540 x = 3780/540

Step 5: Simplify the fraction x = 7

So, the solution to the equation is x = 7.

2. (7x-3)/4 = (5-2x)/6

Step 1: Cross-multiply to eliminate the fractions 6 * (7x - 3) = 4 * (5 - 2x)

Step 2: Expand the expressions 42x - 18 = 20 - 8x

Step 3: Move the variable terms to one side and constant terms to the other side 42x + 8x = 20 + 18

Step 4: Combine like terms 50x = 38

Step 5: Solve for x x = 38/50

Step 6: Simplify the fraction x = 19/25

So, the solution to the equation is x = 19/25.

3. (5/2)x = 3/(4-x)

Step 1: Cross-multiply to eliminate the fractions (4 - x) * (5/2) = 3

Step 2: Distribute the multiplication on the left side (5/2) * 4 - (5/2) * x = 3

Step 3: Simplify the left side (5/2) * 4 - (5/2) * x = 3 10 - (5/2) * x = 3

Step 4: Move constant terms to the other side

• (5/2) * x = 3 - 10
• (5/2) * x = -7

Step 5: Solve for x x = -7 / (5/2)

Step 6: Simplify the fraction x = -7 * (2/5)

Step 7: Multiply the numbers x = -14/5

So, the solution to the equation is x = -14/5.

5. 2/(6-x) = 4/(5x+3)

Step 1: Cross-multiply to eliminate the fractions 2 * (5x + 3) = 4 * (6 - x)

Step 2: Expand the expressions 10x + 6 = 24 - 4x

Step 3: Move the variable terms to one side and constant terms to the other side 10x + 4x = 24 - 6

Step 4: Combine like terms 14x = 18

Step 5: Solve for x x = 18/14

Step 6: Simplify the fraction x = 9/7

So, the solution to the equation is x = 9/7.