Question

consider the equation below.
$-2(5x + 8) = 14 + 6x$
the equation was solved using the following steps.
step 1: $-10x - 16 = 14 + 6x$
step 2: $-16x - 16 = 14$
step 3: $-16x = 30$
step 4: $x = \frac{30}{-16}$
step 5: $x = -\frac{15}{8}$
complete the statements below with the process used to achieve steps 1-4
step 1 -2 to 5x and 8.
step 2 6x
step 3 16
step 4 -16

Explanation:

Step 1: Identify Step 1 Process

To get from \(-2(5x + 8)\) to \(-10x - 16\), we use the Distributive Property (multiply \(-2\) to \(5x\) and \(8\)).

Step 2: Identify Step 2 Process

To get from \(-10x - 16 = 14 + 6x\) to \(-16x - 16 = 14\), we Subtract \(6x\) from both sides (to eliminate \(6x\) on the right).

Step 3: Identify Step 3 Process

To get from \(-16x - 16 = 14\) to \(-16x = 30\), we Add 16 to both sides (to isolate the term with \(x\)).

Step 4: Identify Step 4 Process

To get from \(-16x = 30\) to \(x = \frac{30}{-16}\), we Divide by \(-16\) on both sides (to solve for \(x\)).

(For the dropdowns, the answers would be:
Step 1: Distribute (or Multiply)
Step 2: Subtract
Step 3: Add
Step 4: Divide)

Answer:

Step 1: Distribute (Multiply) \(-2\) to \(5x\) and \(8\).
Step 2: Subtract \(6x\) from both sides.
Step 3: Add \(16\) to both sides.
Step 4: Divide both sides by \(-16\).

(If the dropdowns expect specific terms like "Distributive Property", "Subtract \(6x\)", "Add \(16\)", "Divide by \(-16\)", those are the processes.)