Question

matching equivalent expressions
match each pair of equivalent expressions on the left with the appropriate property on the right.
4(x + 5) = 4x + 20
2 + 7x = 7x + 2
3(x × 4) = (3x) × 4
associative property
distributive property
commutative property

Explanation:

Step1: Analyze \(4(x + 5)=4x + 20\)

The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = 4\), \(b=x\), \(c = 5\), so \(4(x + 5)=4\times x+4\times5 = 4x + 20\). So this matches the distributive property.

Step2: Analyze \(2 + 7x=7x + 2\)

The commutative property of addition states that \(a + b=b + a\). Here, \(a = 2\), \(b = 7x\), so \(2+7x=7x + 2\). So this matches the commutative property.

Step3: Analyze \(3(x\times4)=(3x)\times4\)

The associative property of multiplication states that \(a(b\times c)=(a\times b)c\). Here, \(a = 3\), \(b=x\), \(c = 4\), so \(3(x\times4)=(3x)\times4\). So this matches the associative property.

Answer:

• \(4(x + 5)=4x + 20\) matches distributive property
• \(2 + 7x=7x + 2\) matches commutative property
• \(3(x\times4)=(3x)\times4\) matches associative property