Question

determine whether the expressions are equivalent or not equivalent.

	equivalent	not equivalent
$10x - 6$ and $4x$	$\bigcirc$	$\bigcirc$
$5x + 10$ and $5(x + 10)$	$\bigcirc$	$\bigcirc$
$4a + 12 - a$ and $3(a + 4)$	$\bigcirc$	$\bigcirc$

Explanation:

1. For \(25 - x\) and \(x - 25\)

Step1: Analyze the expressions

\(25 - x\) is a linear expression with a constant term \(25\) and a variable term \(-x\), while \(x - 25\) has a variable term \(x\) and a constant term \(-25\). We can also rewrite \(x - 25\) as \(-(25 - x)\) (by factoring out \(-1\)). So \(x - 25=- (25 - x)\), which means they are negatives of each other, not equivalent.

Step1: Analyze the terms

\(10x - 6\) has a term with \(x\) (coefficient \(10\)) and a constant term \(-6\), while \(4x\) only has a term with \(x\) (coefficient \(4\)). The first expression has a non - zero constant term and a different coefficient for \(x\) compared to the second expression. So they are not equivalent.

Step1: Expand \(5(x + 10)\)

Using the distributive property \(a(b + c)=ab+ac\), where \(a = 5\), \(b=x\) and \(c = 10\), we get \(5(x + 10)=5x+5\times10=5x + 50\).

Step2: Compare with \(5x + 10\)

The expression \(5x + 10\) has a constant term of \(10\), while the expanded form of \(5(x + 10)\) has a constant term of \(50\). So they are not equivalent.

Answer:

Not Equivalent (select the circle under "Not Equivalent" for \(25 - x\) and \(x - 25\))

2. For \(10x - 6\) and \(4x\)