2(2x-7)-16=3(-x-7)-11

I'll be glad to check your answer, Tim.

1st step: lose the parentheses:

2(2x-7)-16=3(-x-7)-11
4x-14-16 = -3x-21-11
. . .

To solve the equation 2(2x - 7) - 16 = 3(-x - 7) - 11, we will follow these steps:

Step 1: Distribute the values inside the parentheses.
Step 2: Simplify both sides of the equation.
Step 3: Combine like terms.
Step 4: Isolate the variable term.
Step 5: Solve for the variable.
Step 6: Check your solution.

Let's go through each step in detail:

Step 1: Distribute the values inside the parentheses.

On the left side, we distribute 2 to both terms inside the parentheses:
2 * 2x = 4x
2 * -7 = -14

So the left side becomes: 4x - 14 - 16

On the right side, we distribute 3 to both terms inside the parentheses:
3 * -x = -3x
3 * -7 = -21

So the right side becomes: -3x - 21 - 11

Now the equation looks like: 4x - 14 - 16 = -3x - 21 - 11

Step 2: Simplify both sides of the equation.

On the left side, we can combine -14 and -16:
-14 - 16 = -30

So the left side simplifies to: 4x - 30

On the right side, we can combine -21 and -11:
-21 - 11 = -32

So the right side simplifies to: -3x - 32

Now the equation becomes: 4x - 30 = -3x - 32

Step 3: Combine like terms.

Move all the terms containing x to one side and all the constant terms to the other side:

Add 3x to both sides:
4x - 3x - 30 = -3x + 3x - 32

Simplifying, we get: x - 30 = -32

Step 4: Isolate the variable term.

To isolate x, we need to get rid of the constant term -30 on the left side. We can do this by adding 30 to both sides:

x - 30 + 30 = -32 + 30

Simplifying, we get: x = -2

Step 5: Solve for the variable.

Therefore, x = -2 is our solution.

Step 6: Check your solution.

To check if our solution is correct, substitute x = -2 back into the original equation:

2(2x - 7) - 16 = 3(-x - 7) - 11

Substituting x = -2:
2(2(-2) - 7) - 16 = 3(-(-2) - 7) - 11

Simplifying both sides, we get:
2(-4 - 7) - 16 = 3(2 - 7) - 11
2(-11) - 16 = 3(-5) - 11
-22 - 16 = -15 - 11
-38 = -26

Since the equation is not true when x = -2, it means that our solution is incorrect or that there is no solution to the equation. Please double-check your initial equation and the steps used.