Question

A) 4(-8m + 5) = -32m - 26

B) -3(x - 1) + 8(x - 3) = 6x + 7 - 5x
C) 8x + 9 - 2x = 3x + 3(3 + 2x)
D) -8n + 4(1 + 5n) = -6n - 14
Solve these equations.

Answer 1

Equations A, B, C, and D were each solved using the distributive property and combining like terms. Equation A had no solution, B had x=7, C had infinitely many solutions, and D had n=-1.

Step-by-step explanation:

To solve the given equations, we will use the distributive property, combine like terms, and isolate the variable to find its value.

1. A) 4(-8m + 5) = -32m - 26
   
   Apply the distributive property: -32m + 20 = -32m - 26
   
   Since -32m on both sides cancel out, we have 20 = -26, which is not true. Thus, there is no solution.

2. B) -3(x - 1) + 8(x - 3) = 6x + 7 - 5x
   
   Apply the distributive property: -3x + 3 + 8x - 24 = x + 7
   
   Combine like terms: 5x - 21 = x + 7
   
   Subtract x from both sides: 4x - 21 = 7
   
   Add 21 to both sides: 4x = 28
   
   Divide by 4: x = 7

3. C) 8x + 9 - 2x = 3x + 3(3 + 2x)
   
   Combine like terms on the left: 6x + 9 = 3x + 3(3 + 2x)
   
   Apply the distributive property: 6x + 9 = 3x + 9 + 6x
   
   Combine like terms: 3x cancels out, and we have 9 = 9, which is true for all x values. So, there are infinitely many solutions.

4. D) -8n + 4(1 + 5n) = -6n - 14
   
   Apply the distributive property: -8n + 4 + 20n = -6n - 14
   
   Combine like terms: 12n + 4 = -6n - 14
   
   Add 6n to both sides: 18n + 4 = -14
   
   Subtract 4 from both sides: 18n = -18
   
   Divide by 18: n = -1