Question

Solve the equation:

2x+10=−4(x+10)

Enter equivalent equations below as you solve the equation. Be sure that your last entry is the solution to the equation and in simplest form. You do not need to use all rows of the table.

a) 2x+10=−4x-40
b) 2x+10=−4x−10
c) 2x+10=−4x+40
d) 2x+10=−4x+10

Answer 1

To solve 2x + 10 = -4(x + 10), expand and simplify to get 2x + 10 = -4x - 40. Then add 4x to both sides, subtract 10, and finally divide by 6 to get x = -25/3.

Step-by-step explanation:

To solve the equation 2x + 10 = -4(x + 10), we start by expanding the right side and simplifying the equation. We get:

2x + 10 = -4x - 40

This matches option (a), so b, c, and d are incorrect. Now, we follow these steps:

1. Add 4x to both sides to get all the x terms on one side:
   2x + 4x + 10 = -40
2. Combine like terms:
   6x + 10 = -40
3. Subtract 10 from both sides to get the x terms by itself:
   6x = -50
4. Divide both sides by 6 to solve for x:
   x = -50 / 6

Hence, the solution to the equation in simplest form is x = -50 / 6 or x = -25 / 3.

Answer 2

a) 2x+10=−4x-40

Step-by-step explanation:

2x+10 =−4(x+10)

2x+10 =−4x-40 [Remove brackets by multiplying by -4]

6x+10 = -40 [add 4x to both sides]

6x = -50 [subtract 10 from both sides]

x = - (50/6) [divide by 6 on both sides]

x = - 48 and 1/3

Answer option a) matches the highlighted expression.