Question

examine the algebraic expression.
$15.2 + \frac{x}{6} - 5.5y + \frac{5}{6}x + 4z - x$
which terms can you combine? select all th
\\(\square\\) 15.2
\\(\square\\) \\(\frac{1}{6}x\\)
\\(\square\\) -5.5y
\\(\square\\) \\(\frac{5}{6}x\\)
\\(\square\\) 4z
\\(\square\\) -x

Explanation:

Step1: Identify like terms

Like terms are terms with the same variable (or no variable for constants) raised to the same power. Here, the terms with \( x \) are \( \frac{x}{6} \) (which is \( \frac{1}{6}x \)), \( \frac{5}{6}x \), and \( -x \). The other terms (\( 15.2 \), \( -5.5y \), \( 4z \)) have different variables or are constants, so they can't be combined with the \( x \)-terms or each other.

Step2: Confirm the \( x \)-terms

• \( \frac{1}{6}x \) (from \( \frac{x}{6} \))
• \( \frac{5}{6}x \)
• \( -x \) (which is \( -1x \))

These three terms have the same variable \( x \) with an exponent of 1, so they are like terms and can be combined. The other terms (15.2, -5.5y, 4z) have different variables or are constants, so they can't be combined with the \( x \)-terms or each other.

Answer:

The terms that can be combined are \( \frac{1}{6}x \) (i.e., \( \frac{x}{6} \)), \( \frac{5}{6}x \), and \( -x \). So the correct options to select are:

• \( \frac{1}{6}x \) (the box next to \( \frac{1}{6}x \))
• \( \frac{5}{6}x \) (the box next to \( \frac{5}{6}x \))
• \( -x \) (the box next to \( -x \))