Question

А) (х-1/4)+3 1/12=7 1/3. б) 6 2/3-(х+1/4)=2 1/6

Answer 1

А) (х-1/4)+3 1/12=7 1/3
x-1/4+ 37/12=22/3
x=3*22/3+4*1/4-37/12
x=33/12=2 9/12= 2 3/4
x=2 3/4

б) 6 2/3-(х+1/4)=2 1/6
20/3-x-1/4=13/6
-x=2*13/6-4*20/3+3*1/4
-x=-51/12= -4 3/12=-4 1/4
x=4 1/4

Answer 2

To solve the equations, let's start with each one:

а) (х - 1/4) + 3 1/12 = 7 1/3

Step 1: Let's simplify the fractions on the left side: 3 1/12 = 3 + 1/12 = 3 1/12

Now, the equation becomes: (х - 1/4) + 3 1/12 = 7 1/3

Step 2: Combine the integer and fractional parts separately: (х - 1/4) + 3 + 1/12 = 7 + 1/3

Step 3: Combine the integer and fractional parts of 7 1/3: (х - 1/4) + 3 + 1/12 = 7 + 4/12

Step 4: Combine the integer and fractional parts of 3 1/12: (х - 1/4) + 3 + 1/12 = 6 + 1/12

Step 5: Now, simplify the equation: х + 3 - 1/4 + 1/12 = 6 + 1/12

Step 6: Combine the constants and fractions on the left side: х + 3 - (1/4 - 1/12) = 6 + 1/12

Step 7: Calculate the fractions in the parentheses: х + 3 - (3/12 - 1/12) = 6 + 1/12

Step 8: Continue to simplify: х + 3 - 2/12 = 6 + 1/12

Step 9: Convert the fractions into a common denominator: х + 3 - 1/6 = 6 + 1/12

Step 10: Subtract 3 from both sides to isolate х: х - 1/6 = 6 + 1/12 - 3

Step 11: Combine the constants on the right side: х - 1/6 = 6 - 2/12

Step 12: Convert 6 to twelfths: х - 1/6 = 72/12 - 2/12

Step 13: Combine the constants on the right side: х - 1/6 = 70/12

Step 14: Now, add 1/6 to both sides to solve for x: х = 70/12 + 1/6

Step 15: Convert 1/6 to twelfths and add the fractions: х = 70/12 + 2/12

Step 16: Combine the fractions on the right side: х = 72/12

Step 17: Simplify the fraction (divide numerator and denominator by their greatest common divisor, which is 12 in this case): х = 6

So, the solution for the first equation is x = 6.

Let's move on to the second equation:

б) 6 2/3 - (х + 1/4) = 2 1/6

Step 1: Convert the mixed numbers to improper fractions: 6 2/3 = 20/3 2 1/6 = 13/6

Now, the equation becomes: 20/3 - (х + 1/4) = 13/6

Step 2: To simplify the equation, find a common denominator for 3 and 6, which is 6: 20/3 - (2х + 1)/4 = 13/6

Step 3: Now, let's eliminate the fractions by multiplying both sides by the common denominator, 6: 6 * (20/3) - 6 * ((2х + 1)/4) = 6 * (13/6)

Step 4: Simplify the equation further: 40 - 3(2х + 1) = 13

Step 5: Distribute the -3 on the left side: 40 - 6х - 3 = 13

Step 6: Combine the constants on the left side: 37 - 6х = 13

Step 7: To isolate х, subtract 37 from both sides: -6х = 13 - 37

Step 8: Simplify the right side: -6х = -24

Step 9: Finally, divide both sides by -6 to solve for х: х = -24 / -6

Step 10: Simplify the fraction: х = 4

So, the solution for the second equation is x = 4.

To summarize:

а) x = 6 б) x = 4