Question

− 3 ( 4 x + 3 ) + 4 ( 6 x + 1 ) = k

Answer 1

To solve the given equation for k, distribute the numbers outside the parentheses, combine like terms, and the resulting expression for k is 12x - 5.

Step-by-step explanation:

The student's question involves simplifying a linear equation and finding the constant k. The equation given is:
− 3 ( 4x + 3 ) + 4 ( 6x + 1 ) = k

To solve for k, we must first distribute the numbers outside the parentheses and then combine like terms:

1. Distribute − 3 to the terms inside the first parentheses: − 3 × 4x − 3 × 3 = − 12x − 9.
2. Distribute 4 to the terms inside the second parentheses: 4 × 6x + 4 × 1 = 24x + 4.
3. Now, combine the x terms and constant terms: (− 12x + 24x) + (− 9 + 4) = 12x − 5.
4. Finally, to solve for k, we set the equation equal to the expression representing k:
   12x − 5 = k.

Therefore, the constant k is represented by the expression 12x − 5.