Question

7 (\frac{2}{3}(x + 18 - 2x))
8 (\frac{3}{4}(16x - 27 - 1))
9 (-12left(\frac{5}{6}x - 5
ight) + 2x)
determine which expressions, if any, are equivalent. show your work.
10 (4(x - 3)) (6x - 2(x - 3)) (x + 3(x - 2) - 6)

Explanation:

Step1: Simplify \(4(x - 3)\)

Using the distributive property \(a(b - c)=ab - ac\), we get \(4x-12\).

Step2: Simplify \(6x - 2(x - 3)\)

First, distribute the \(-2\) in \(-2(x - 3)\): \(-2x + 6\). Then combine like terms with \(6x\): \(6x-2x + 6=4x + 6\).

Step3: Simplify \(x + 3(x - 2)-6\)

Distribute the \(3\) in \(3(x - 2)\): \(3x-6\). Then combine all terms: \(x+3x - 6-6 = 4x-12\).

Answer:

The expressions \(4(x - 3)\) and \(x + 3(x - 2)-6\) are equivalent (both simplify to \(4x - 12\)), and \(6x - 2(x - 3)\) is not equivalent to them (it simplifies to \(4x + 6\)).