Question

So far in this course, you have solved single-variable equations like 3x+7=-x-3. Consider this change to that equation: 3(x+7)=-x-3. What is different about the equations? How will the changes made to the original equation change the steps needed to solve the equation?

Answer 1

The main difference between the two equations is that the second equation has parentheses around the expression (x+7), indicating that the entire expression should be multiplied by 3.

To solve the second equation, we will need to first distribute the 3 to the expression inside the parentheses, resulting in 3x + 21 on the left-hand side of the equation. We can then proceed with solving the equation as we did before by adding x to both sides and subtracting 3 from both sides:

3x + 21 = -x - 3
4x = -24
x = -6

So the solution to the second equation is x = -6.

In summary, the change to the original equation requires us to first distribute the coefficient of 3 to the expression inside the parentheses before proceeding with the usual steps of solving the equation.

Answer 2

Answer below

Explanation:

For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2

The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6