7 Georgia is given the equation 4(k - 5) + 3k = 1 , and asked to solve for k. Which of the following is the first step Georgia should perform to solve the equation? А B D Subtract 3k from both sides . Multiply 4 to k, and multiply 4 to -5. Add -4 to both sides Combine 4k and 3k.
To solve the equation 4(k - 5) + 3k = 1 for k, Georgia can follow these steps:
1. Distribute the 4 to both terms inside the parentheses: 4k - 20 + 3k = 1
(The -5 is multiplied by 4 and becomes -20)
Now, let's consider the options provided:
A) Subtract 3k from both sides.
This step is not the first step Georgia should perform because it would result in combining the k terms before distributing the 4 to the terms inside the parentheses. So option A is incorrect.
B) Multiply 4 to k, and multiply 4 to -5.
This step is also not the first step Georgia should perform. As mentioned earlier, the distribution of 4 to the terms inside parentheses should be done first. So option B is incorrect.
D) Combine 4k and 3k.
This step is not the first step Georgia should perform either. Before combining like terms, Georgia needs to distribute the 4 to the terms inside parentheses. So option D is incorrect.
The correct first step that Georgia should perform is:
C) Add -4 to both sides.
This is the correct step because it will eliminate the constant term (-20) on the left side of the equation. The equation becomes: 4k + 3k - 20 = 1
Therefore, the correct answer is option C) Add -4 to both sides.
distribute the 4 over the (k - 5)
4k - 20 + 3k = 1 ... 7k = 21