Question

1/6/1/4х - 1/3 - 3/8 = 1/40 2) 1/4/3/4х - 1/2 + 2/5 = 1/2

Answer 1

Ответ:

1.

1/6:(1/4х-1/3)-3/8=1/40

1/6:(1/4х-1/3)=1/40+3/8

1/6:(1/4х-1/3)=1/40+15/40

1/6:(1/4х-1/3)=2/5

1/4х-1/3=1/6:2/5

1/4х-1/3=5/12

1/4х=5/12+1/3

1/4х=5/12+4/12

1/4х=9/12

х=9/12:1/4

х=3

2.

1\4 : 3\4x -1\2 + 2\5 =1\2

1\4 : 3\4X = 1\2 +1\2 -2\5

1\2 + 1\2 -2\5 =5\10 + 5\10 -4\10 = 6\10 =3\5

1\4 : 3\4x =3\5

3\4x = 1\4 :3\5 

1\4  :3\5 = 1\4 x 5\3 =5\12

3\4x= 5\12

x = 5\12 : 3\4 = 5\12 x4\3 =5\9

x = 5\9

Пошаговое объяснение:

Answer 2

To solve these equations involving fractions, we need to find the value of 'x' that satisfies the equations. Let's take them one by one:

1. $\frac{1}{6x} - \frac{1}{3} - \frac{3}{8} = \frac{1}{40}$

Step 1: Find a common denominator for the fractions. The common denominator for 6x, 3, and 8 is 24x.

Step 2: Rewrite the equation with the common denominator.

$\frac{4x}{24x} - \frac{8}{24x} - \frac{9x}{24x} = \frac{1}{40}$

Step 3: Combine the fractions on the left side of the equation.

$\frac{4x - 8 - 9x}{24x} = \frac{1}{40}$

Step 4: Combine the x terms.

$\frac{-5x - 8}{24x} = \frac{1}{40}$

Step 5: Cross-multiply to eliminate the fractions.

$40(-5x - 8) = 24x$

Step 6: Solve for 'x'.

$-200x - 320 = 24x$

$-200x - 24x = 320$

$-224x = 320$

$x = \frac{320}{-224}$

$x = -\frac{20}{14}$

Simplifying the fraction:

$x = -\frac{10}{7}$

Therefore, the value of 'x' that satisfies the first equation is $x = -\frac{10}{7}$.

2. $\frac{1}{4} \div \frac{3}{4x} - \frac{1}{2} + \frac{2}{5} = \frac{1}{2}$

Step 1: Perform the division.

$\frac{1}{4} \times \frac{4x}{3} - \frac{1}{2} + \frac{2}{5} = \frac{1}{2}$

Step 2: Simplify the expression on the left side.

$\frac{4x}{12} - \frac{1}{2} + \frac{2}{5} = \frac{1}{2}$

Step 3: Find a common denominator for the fractions.

The common denominator for 12, 2, and 5 is 60.

Step 4: Rewrite the equation with the common denominator.

$\frac{20x}{60} - \frac{30}{60} + \frac{24}{60} = \frac{30}{60}$

Step 5: Combine the fractions on the left side of the equation.

$\frac{20x - 30 + 24}{60} = \frac{30}{60}$

Step 6: Combine the terms.

$\frac{20x - 6}{60} = \frac{30}{60}$

Step 7: Cross-multiply to eliminate the fractions.

$60(20x - 6) = 30$

Step 8: Solve for 'x'.

$1200x - 360 = 30$

$1200x = 390$

$x = \frac{390}{1200}$

Since the numerator and denominator can be divided by 30:

$x = \frac{13}{40}$

Therefore, the value of 'x' that satisfies the second equation is $x = \frac{13}{40}$