Final answer:
The equations involve solving linear equations by isolating variables and working with fractions. The solutions for these algebraic equations are found by performing arithmetic operations and simplifying. Equations (c) and (d) result in no solution or are dependent.
Step-by-step explanation:
The subject of this question is mathematics, specifically involving solving linear equations. The equations provided are all algebraic and require isolating the variable to find its value. Let's solve each equation step-by-step:
- Solving equation (a): K + 5/3 = -7/4.
- First, subtract 5/3 from both sides to isolate the variable K:
- K = -7/4 - 5/3
- To combine the fractions, find a common denominator, which in this case is 12:
- K = (-21/12) - (20/12)
- Combine the fractions:
- K = -41/12
- Solving equation (b): -16 = 40 - 3p.
- First, add 3p to both sides of the equation:
- 3p - 16 = 40
- Now, subtract 40 from both sides:
- 3p = -16 - 40
- Combine the numbers:
- 3p = -56
- Finally, divide both sides by 3 to solve for p:
- p = -56/3
- Solving equation (c): 13 - 2(4r - 5) = 5 - (7 + 8r).
- First, distribute the -2 and -1 through the parentheses:
- 13 - 8r + 10 = 5 - 7 - 8r
- Combine like terms:
- -8r + 23 = -8r - 2
- Since the terms with r cancel each other out, this equation has no solution or is dependent (all real numbers satisfy it).
- Solving equation (d): 2(2v - 9) + 1 = -5v - 17 + 9v.
- First, distribute the 2:
- 4v - 18 + 1 = 4v - 16
- Combine like terms on the left side:
- 4v - 17 = 4v - 16
- Again, since the terms with v cancel each other out, the equation has no solution or is dependent.