Question

card sort
group the equivalent expressions. one expression will have no group.
24 - 8x
-24 + 8x
8x - 24
8(x - 3)
\frac{1}{2}(16x - 48)
-8(x - 24)
-4(-6 + 2x)

Explanation:

Step1: Simplify \(8(x - 3)\)

Using the distributive property \(a(b - c)=ab - ac\), we get \(8x-24\).

Step2: Simplify \(\frac{1}{2}(16x - 48)\)

Using the distributive property \(\frac{1}{2}\times16x-\frac{1}{2}\times48 = 8x - 24\).

Step3: Simplify \(-4(-6 + 2x)\)

Using the distributive property \((-4)\times(-6)+(-4)\times2x=24 - 8x\).

Step4: Simplify \(-8(x - 24)\)

Using the distributive property \(-8x+192\) (this has no equivalent in the other expressions for the main group we are forming here, but let's focus on the equivalent ones first).

Step5: Analyze \(-24 + 8x\)

Rearrange terms: \(8x-24\), which is the same as the result from Step1 and Step2.

Step6: Analyze \(24 - 8x\)

This is the same as the result from Step3.

Now, let's group the equivalent expressions:

• Group 1 (equivalent to \(8x - 24\)): \(8x - 24\), \(8(x - 3)\), \(\frac{1}{2}(16x - 48)\), \(-24 + 8x\)
• Group 2 (equivalent to \(24 - 8x\)): \(24 - 8x\), \(-4(-6 + 2x)\)
• The expression \(-8(x - 24)\) has no group (or is in its own group as it doesn't match the others)

Answer:

• Equivalent to \(8x - 24\): \(8x - 24\), \(8(x - 3)\), \(\frac{1}{2}(16x - 48)\), \(-24 + 8x\)
• Equivalent to \(24 - 8x\): \(24 - 8x\), \(-4(-6 + 2x)\)
• No group: \(-8(x - 24)\)