Question

Enter the numbers that make the algebraic expressions equivalent.(1 point)
Expression 1: 4x+5(x−2) +____

Expression 2:
____x−11−x+9

Answer 1

To make the two algebraic expressions equivalent, we can simplify both expressions step by step.

### Expression 1:
\[ 4x + 5(x - 2) + \_\_\_ \]

First, let's simplify \(5(x - 2)\):

\[
5(x - 2) = 5x - 10
\]

Now, substitute this back into Expression 1:

\[
4x + 5x - 10 + \_\_\_
\]

Combine like terms:

\[
(4x + 5x) - 10 + \_\_ = 9x - 10 + \_\_
\]

Let's denote the blank with \(A\):

\[
9x - 10 + A
\]

### Expression 2:
\[ \_\_x - 11 - x + 9 \]

Let's denote the blank with \(B\):

\[
Bx - 11 - x + 9
\]

Now combine like terms:

\[
(B - 1)x + (-11 + 9) = (B - 1)x - 2
\]

### Now, we want the two expressions to be equivalent:

From Expression 1:
\[
9x - 10 + A \Rightarrow 9x + (A - 10)
\]

From Expression 2:
\[
(B - 1)x - 2 \Rightarrow (B - 1)x + (-2)
\]

To make the \(x\) coefficients equal and the constant terms equal, we set up the following equations:

1. \(B - 1 = 9\)
2. \(A - 10 = -2\)

### Solve for \(B\):
\[
B - 1 = 9 \implies B = 9 + 1 = 10
\]

### Solve for \(A\):
\[
A - 10 = -2 \implies A = -2 + 10 = 8
\]

### Therefore:
- The number for Expression 1 (blank) is **8**.
- The number for Expression 2 (blank) is **10**.

The completed expressions are:
- Expression 1: \( 4x + 5(x - 2) + 8 \)
- Expression 2: \( 10x - 11 - x + 9 \)

So the final answers are:
- **8** for the first blank
- **10** for the second blank