Solve the equations symbolically.

3x+7/4 + 3x-7/5 =-8/5

6(7x-1)+5=24+3x

How do I go about solving them?

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To solve the given equations symbolically, follow these steps:

Equation 1: 3x + 7/4 + 3x - 7/5 = -8/5

1. Combine like terms: 3x + 3x + 7/4 - 7/5 = -8/5
(Combine the x terms and the constant terms separately)

2. Find a common denominator for the fractions involved (4 and 5 in this case): 20

3. Multiply each term by the common denominator to clear the fractions:
15x + 15x + 35/20 - 28/20 = -8/5
(Multiply each term by 20 to eliminate the fractions)

4. Simplify the equation: 30x + 30x + 7/20 = -8/5

5. Combine like terms again: 60x + 7/20 = -8/5

6. Move the constant term to the other side of the equation:
60x = -8/5 - 7/20
(Find a common denominator)

7. Simplify the right side of the equation: -8/5 - 7/20 = -32/20 - 7/20 = -39/20

8. Divide both sides of the equation by the coefficient of x (60) to solve for x:
x = (-39/20) / 60
(Divide both sides by 60)

9. Simplify the result: x = -39/20 / 60 = -39/20 * 1/60 = -39/120

Therefore, the solution to equation 1 is x = -39/120.

Equation 2: 6(7x - 1) + 5 = 24 + 3x

1. Distribute the 6 to the terms inside the parentheses: 42x - 6 + 5 = 24 + 3x

2. Combine like terms: 42x - 1 = 24 + 3x

3. Move the constant term to the other side of the equation: 42x - 3x = 24 + 1
(Keep the variable terms on one side and the constant terms on the other side)

4. Simplify the equation: 39x = 25

5. Divide both sides of the equation by the coefficient of x (39) to solve for x:
x = 25 / 39
(Divide both sides by 39)

Therefore, the solution to equation 2 is x = 25/39.