Question

combining like terms - item 33821
find equivalent expressions of $3 + 2x - 9 - 4x + 11 + 5x - x$.
choose three expressions.
$2x + 5$ $12x + 23$
$3x - 2 - x + 1$ $4x + 11 - 2x - 6$
$2x - 1 - 4x + 4$ $2x - x + 3 + x - 3 + 5$

Explanation:

Step1: Combine constant terms

Constant terms: \(3 - 9 + 11\)
\(3 - 9 + 11 = (3 + 11) - 9 = 14 - 9 = 5\)

Step2: Combine \(x\)-terms

\(x\)-terms: \(2x - 4x + 5x - x\)
\(2x - 4x + 5x - x = (2 - 4 + 5 - 1)x = 2x\)

Step3: Original expression simplifies to

\(2x + 5\)
Now check each option:

• \(2x + 5\): Matches, so this is equivalent.
• \(12x + 23\): Does not match, eliminate.
• \(3x - 2 - x + 1\): Combine terms: \((3x - x)+(-2 + 1)=2x - 1\) → No. Wait, recalculate: \(3x - x = 2x\), \(-2 + 1 = -1\)? Wait no, \(3x - 2 - x + 1=(3x - x)+(-2 + 1)=2x - 1\)? Wait, no, maybe I miscalculated. Wait, original is \(2x + 5\). Wait, let's re - check \(3x - 2 - x + 1\): \(3x - x = 2x\), \(-2 + 1=-1\), so \(2x - 1\). Not equal. Wait, maybe another option.
• \(4x + 11 - 2x - 6\): Combine terms: \((4x - 2x)+(11 - 6)=2x + 5\). Yes, this matches.
• \(2x - 1 - 4x + 4\): Combine terms: \((2x - 4x)+(-1 + 4)=-2x + 3\). No.
• \(2x - x + 3 + x - 3 + 5\): Combine terms: \((2x - x + x)+(3 - 3 + 5)=2x + 5\). Yes, this matches.

Wait, earlier mistake with \(3x - 2 - x + 1\). Let's recalculate \(3x - 2 - x + 1\): \(3x - x=2x\), \(-2 + 1=-1\), so \(2x - 1\), which is not equal. So the three equivalent are:

1. \(2x + 5\)
2. \(4x + 11 - 2x - 6\)
3. \(2x - x + 3 + x - 3 + 5\)

Answer:

The three equivalent expressions are:

• \(2x + 5\)
• \(4x + 11 - 2x - 6\)
• \(2x - x + 3 + x - 3 + 5\)