Question

Enter the number that makes the algebraic expression equivalent expression 1 4x + 5 (x - 2) + blank expression 2 blank x - 11 - x + 9

Answer 1

To find the number that makes the algebraic expression equivalent, let's first simplify both expressions.

**Expression 1:**
\[ 4x + 5(x - 2) + \text{blank} \]

Distributing 5 into \((x - 2)\):
\[ 4x + 5x - 10 + \text{blank} \]
Combine like terms:
\[ (4x + 5x) - 10 + \text{blank} = 9x - 10 + \text{blank} \]

**Expression 2:**
\[ \text{blank} x - 11 - x + 9 \]

Combine like terms:
\[ \text{blank} x - x - 11 + 9 = (\text{blank} - 1)x - 2 \]

Now we can set the two simplified expressions equal to each other:
\[ 9x - 10 + \text{blank} = (\text{blank} - 1)x - 2 \]

To make this equation true for all \(x\), we can equate the coefficients of \(x\) and the constant terms.

1. For the coefficients of \(x\):
\[ 9 = \text{blank} - 1 \]
Therefore,
\[ \text{blank} = 10 \]

2. For the constant terms:
\[ -10 + 10 = -2 \]
This simplifies to \(0 = -2\), which is not valid, indicating there is no need to check, as the values are consistent.

Thus, the missing number (blank) is \(10\).