Question

1/3x+1=2-1/6x 1/4x-3=1/8x+5

Answer 1

1/3х+1=2-1/6х
1/3х+1/6х=2-1
2/6х+1/6х=1
3/6х=1
1/2х=1
х=1:1/2
х=1*2/1
х=2

1/4х-3=1/8х+5
1/4х-1/8х=3+5
2/8х-1/8х=8
1/8х=8
х=8:1/8
х=8*8/1
х=64

Answer 2

Let's solve the given equations step by step:

Equation 1:

1/3x + 1 = 2 - 1/6x

To simplify the equation, let's first get rid of the fractions by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 6:

6 * (1/3x) + 6 * 1 = 6 * 2 - 6 * (1/6x)

2x + 6 = 12 - x

Now, let's group the x terms on one side and the constant terms on the other side:

2x + x = 12 - 6

3x = 6

Divide both sides by 3 to solve for x:

x = 2

Therefore, the solution to the first equation is x = 2.

Equation 2:

1/4x - 3 = 1/8x + 5

Again, let's eliminate the fractions by multiplying the equation by the LCM of the denominators, which is 8x:

8x * (1/4x) - 8x * 3 = 8x * (1/8x) + 8x * 5

2 - 24x = 1 + 40x

Let's group the x terms on one side and the constant terms on the other side:

-24x - 40x = 1 - 2

-64x = -1

Divide both sides by -64 to solve for x:

x = (-1) / (-64)

x = 1/64

Therefore, the solution to the second equation is x = 1/64.

In summary, the solutions to the given equations are:

Equation 1: x = 2 Equation 2: x = 1/64