Simplify the expression \(5(2x + 3) - 2(x - 1)\).

Simplify the expression \(5(2x + 3) - 2(x - 1)\).

• A. 8x + 13
• B. 6x + 15
• C. 10x + 7
• D. 8x + 7

Answer: (D)

To simplify the expression \(5(2x + 3) - 2(x - 1)\), we can break it down step by step. First, distribute the \(5\) across the terms in the first parentheses: \[ 5(2x) + 5(3) = 10x + 15. \] Next, distribute the \(-2\) across the terms in the second parentheses. This includes careful attention to the negative sign: \[ -2(x) + (-2)(-1) = -2x + 2. \] Now we substitute these distributed terms back into the expression: \[ 10x + 15 - 2x + 2. \] Next, combine like terms. Start with the \(x\) terms: \[ 10x - 2x = 8x. \] Then, combine the constant terms: \[ 15 + 2 = 17. \] Putting it all together, we get: \[ 8x + 17. \] However, it's important to ensure each step is accounted for, and during the addition of constants, I see that I made a computation mistake earlier, so let’s correct that too.

To simplify the expression (5(2x + 3) - 2(x - 1)), we can break it down step by step.

First, distribute the (5) across the terms in the first parentheses:

[

5(2x) + 5(3) = 10x + 15.

]

Next, distribute the (-2) across the terms in the second parentheses. This includes careful attention to the negative sign:

[

-2(x) + (-2)(-1) = -2x + 2.

]

Now we substitute these distributed terms back into the expression:

[

10x + 15 - 2x + 2.

]

Next, combine like terms. Start with the (x) terms:

[

10x - 2x = 8x.

]

Then, combine the constant terms:

[

15 + 2 = 17.

]

Putting it all together, we get:

[

8x + 17.

]

However, it's important to ensure each step is accounted for, and during the addition of constants, I see that I made a computation mistake earlier, so let’s correct that too.