Question

Consider the equation (5(2x - 1))/3 - 4 = 11 This equation looks complicated, but we can unravel all of the operations that have been done to x to produce the output of 11. (a) List the operations that have been done to x (b) Reverse the operations from (a) to solve for the x order in which they have been done.

Answer 1

To solve the equation, list and reverse the mathematical operations applied to x, ensure to maintain balance by performing each step on both sides of the equation. The correct value of x after reversing the operations is 5.

Step-by-step explanation:

To solve the equation (5(2x - 1))/3 - 4 = 11, we need to list the operations applied to x and then reverse them:

1. Multiply x by 2.
2. Subtract 1 from the result of step 1.
3. Multiply the result of step 2 by 5.
4. Divide the result of step 3 by 3.
5. Subtract 4 from the result of step 4 to get the final result, 11.

To reverse these operations and solve for x, we should:

1. Add 4 to both sides of the equation to cancel out the subtraction of 4.
2. Multiply both sides by 3 to undo the division by 3.
3. Divide both sides by 5 to reverse the multiplication by 5.
4. Add 1 to both sides to compensate for the initial subtraction of 1.
5. Finally, divide both sides by 2 to undo the initial multiplication by 2, which gives us x.

When reversing these operations, ensure that whatever you do to one side of the equation, you also do to the other side (balance the equation).

Now let's solve the equation step by step:

1. (5(2x - 1))/3 - 4 + 4 = 11 + 4
2. (5(2x - 1))/3 = 15
3. 5(2x - 1) = 15 * 3
4. 5(2x - 1) = 45
5. (2x - 1) = 45 / 5
6. (2x - 1) = 9
7. 2x - 1 + 1 = 9 + 1
8. 2x = 10
9. x = 10 / 2
10. x = 5

Answer 2

Consider the equation (5(2x - 1))/3 - 4 = 11 This equation looks complicated, but we can unravel all of the operations that have been done to x to produce the output of 11. The value of x = 3.

Step-by-step explanation:

To solve the equation (5(2x - 1))/3 - 4 = 11, we first list the operations that have been done to x.

(a) List the operations that have been done to x:

1. Multiply x by 2 to get 2x.

2. Subtract 1 from 2x to get 2x - 1.

3. Multiply the result of step 2 by 5 to get 5(2x - 1).

4. Divide the result of step 3 by 3 to get (5(2x - 1))/3.

5. Subtract 4 from the result of step 4 to get (5(2x - 1))/3 - 4.

6. Set the result of step 5 equal to 11 to get (5(2x - 1))/3 - 4 = 11.

Now, we reverse the operations from (a) to solve for the x order in which they have been done.

(b) Reverse the operations from (a):

1. Add 4 to both sides of the equation to get (5(2x - 1))/3 = 15.

2. Multiply both sides of the equation by 3 to get 5(2x - 1) = 45.

3. Divide both sides of the equation by 5 to get 2x - 1 = 9.

4. Add 1 to both sides of the equation to get 2x = 10.

5. Divide both sides of the equation by 2 to get x = 5.

6. Subtract integer part from decimal part and round it off if necessary, but in this case, we don't need it as we got an integer value for x, so our final answer is x = 3.