Option C:
The equivalent expression is [tex]8\left(\frac{3}{4} a-1\right)[/tex].
Solution:
Given expression:
[tex]$8\left(\frac{3}{4} a\right)-8[/tex]
To find which expression is equal to the given expression:
Option A: [tex]\frac{3}{4}a[/tex]
After cancelling 4 and 8, we get
[tex]8\left(\frac{3}{4} a\right)-8=2\left(3a)-8[/tex]
= 6a – 8
This is not equivalent expression.
Option B: 6a
By the above calculation, we get 6a –8.
This is not equivalent expression.
Option C: [tex]8\left(\frac{3}{4} a-1\right)[/tex]
[tex]8\left(\frac{3}{4} a\right)-8[/tex]
Two terms have 8 common, so take 8 outside.
[tex]8\left(\frac{3}{4} a\right)-8=8\left(\frac{3}{4} a-1\right)[/tex]
This is the equivalent expression.
Option D: [tex]\frac{3}{4} a-1[/tex]
By the above calculation, we get [tex]8\left(\frac{3}{4} a-1\right)[/tex].
This is not equivalent expression.
Hence Option C is the correct answer.
The equivalent expression is [tex]8\left(\frac{3}{4} a-1\right)[/tex].
