Solve the equation and write down the property you use at each step to simplify the equation. Consider the equation: 4x + 11 = (5x + 34)/2. Be sure to show your work.. Thank You Jiskha..!! :)

4x + 11 = (5x + 34)/2

multiply both sides by 2
4x + 11 = 5x + 34
4x - 5x = 34-11 , obvious steps
-x = 23
x = -23 , divided both sides by -1

To solve the equation 4x + 11 = (5x + 34)/2, we'll first eliminate the fraction by multiplying every term by the denominator, which is 2. This will clear the equation of fractions.

Step 1: Multiply every term by 2.
2 * (4x + 11) = 2 * [(5x + 34)/2]
8x + 22 = 5x + 34

Property used: Multiplication Property of Equality.

Step 2: Simplify both sides of the equation.
8x + 22 - 5x = 5x + 34 - 5x
3x + 22 = 34

Property used: Subtraction Property of Equality.

Step 3: Isolate the variable term on one side by subtracting 22 from both sides.
3x + 22 - 22 = 34 - 22
3x = 12

Property used: Subtraction Property of Equality.

Step 4: Solve for x by dividing both sides by 3.
(3x) / 3 = 12 / 3
x = 4

Property used: Division Property of Equality.

Therefore, the solution to the equation 4x + 11 = (5x + 34)/2 is x = 4.

To solve the equation 4x + 11 = (5x + 34)/2, we will follow the steps below:

Step 1: Distribute the division symbol (/) to the terms inside the parentheses on the right side of the equation:
4x + 11 = 5x/2 + 34/2

Step 2: Simplify the right side by dividing both terms by 2:
4x + 11 = (5/2)x + 17

Step 3: Rearrange the equation by subtracting (5/2)x from both sides:
4x - (5/2)x + 11 = 17

Step 4: Combine like terms by finding a common denominator for the coefficients of x:
(8/2)x - (5/2)x + 11 = 17

Step 5: Simplify the left side of the equation by combining the fractions:
(3/2)x + 11 = 17

Step 6: Isolate the variable term by subtracting 11 from both sides:
(3/2)x = 17 - 11

Step 7: Simplify the right side of the equation:
(3/2)x = 6

Step 8: Solve for x by multiplying both sides by the reciprocal of (3/2), which is (2/3):
x = 6 * (2/3)

Step 9: Simplify the right side to get the final solution for x:
x = 4

To summarize, the steps taken to solve the equation 4x + 11 = (5x + 34)/2 are:
Step 1: Distributive property
Step 2: Simplifying fractions
Step 3: Rearranging terms
Step 4: Combining fractions with a common denominator
Step 5: Simplifying fractions
Step 6: Subtracting
Step 7: Simplifying
Step 8: Multiplying by the reciprocal
Step 9: Simplifying