Question

1) (x+4/21)-4/15=16/352) (x-8/19)-4/57=2/3 

Answer 1

1) (х+4/21)-4/15=16/35
х+4/21=16/35+4/15
х+4/21=76/105
х=56/105

2) (х-8/19)-4/57=2/3
х-8/19=2/3+4/57
х-8/19=42/57
х=1  3/19

Answer 2

To solve these two linear equations, you can follow these steps:

1. (x + 4/21) - 4/15 = 16/35:

First, find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is 105. Rewrite the equation:

(105/21)(x + 4/21) - (105/15)(4/15) = (105/35)(16/35)

Now, simplify the fractions:

5(x + 4/21) - 7(4/15) = 3(16/35)

Now distribute and simplify:

5x + (20/21) - (28/15) = (48/35)

Next, subtract (20/21) and (28/15) from both sides:

5x = (48/35) - (20/21) + (28/15)

To add these fractions, you'll need to find a common denominator. The common denominator is 105:

5x = (72/105) - (100/105) + (196/105)

Now, add the fractions:

5x = (72 - 100 + 196)/105

5x = 168/105

Now, divide both sides by 5 to isolate x:

x = (168/105) / 5 x = (168/105) * (1/5) x = 168/525

Now, simplify the fraction:

x = 56/175

2. (x - 8/19) - 4/57 = 2/3:

First, find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is 57. Rewrite the equation:

(57/19)(x - 8/19) - 4/57 = (19/57)(2/3)

Now, simplify the fractions:

3(x - 8/19) - 4/57 = (38/57)

Now distribute and simplify:

3x - (24/19) - 4/57 = 38/57

Next, add (24/19) and (4/57) to both sides to isolate 3x:

3x = (38/57) + (24/19) + (4/57)

To add these fractions, you'll need to find a common denominator. The common denominator is 57:

3x = (38/57) + (3 * 24/57) + (4/57)

Now, add the fractions:

3x = (38 + 72 + 4)/57

3x = 114/57

Now, divide both sides by 3 to isolate x:

x = (114/57) / 3 x = (114/57) * (1/3) x = 38/57

Now, simplify the fraction:

x = 2/3