Which one of the following is the solution of the equation 5𝑎−23=3𝑎+11 ?ResponsesA 1919B 1717C 1515D 1313E

1. Break Down the Problem

We need to solve the equation $5a - 23 = 3a + 11$ for the variable $a$. This involves isolating the variable on one side of the equation.

2. Relevant Concepts

To isolate $a$, we will use basic algebraic principles, including:

• Adding or subtracting the same value from both sides of the equation.
• Combining like terms.

3. Analysis and Detail

1. Start with the original equation: $5a - 23 = 3a + 11$

2. Subtract $3a$ from both sides: $5a - 3a - 23 = 11$ This simplifies to: $2a - 23 = 11$

3. Next, add $23$ to both sides: $2a - 23 + 23 = 11 + 23$ This simplifies to: $2a = 34$

4. Finally, divide both sides by $2$: $a = \frac{34}{2} = 17$

4. Verify and Summarize

To verify, substitute $a = 17$ back into the original equation:

• Left side: $5(17) - 23 = 85 - 23 = 62$
• Right side: $3(17) + 11 = 51 + 11 = 62$

Both sides are equal, confirming that our solution is correct.

Final Answer

The solution of the equation $5a - 23 = 3a + 11$ is $a = 17$. Thus, the correct response is B 17.