Question

name:
date:
topic:
class:
main ideas/questions notes/examples
parts of an expression
note: if there is a subtraction sign before a term, it is negative!

directions: identify the variable terms, constant terms, and coefficients.
examples

	expression	variable terms	coefficients	constant terms
1.	$4x + 9 - 7x$
2.	$-7a - 1 + 16$
3.	$9 - 6k + 8k + 1$
4.	$r - 14 - 5 + 2r$
5.	$-6 + 7w - w - 13$
6.	$\frac{1}{2}p + 14 - 2 - 9p$
7.	$8x + 3y + 15y$
8.	$-3m + 7n - 14 + 8m$
9.	$-7w + 2u - 11 - 4 + 6w$
10.	$\frac{2}{3}p - \frac{5}{6}q + \frac{1}{4}$

© gina wilson (all things algebra)

Answer:

To solve each example, we identify variable terms (terms with a variable), coefficients (numbers next to variables), and constant terms (terms without a variable) by analyzing each expression:

Example 1: \( 4x + 9 - 7x \)

• Variable Terms: Terms with \( x \): \( 4x, -7x \)
• Coefficients: Numbers next to \( x \): \( 4, -7 \)
• Constant Terms: Term without a variable: \( 9 \)

Example 2: \( -7a - 1 + 16 \)

• Variable Terms: Term with \( a \): \( -7a \)
• Coefficients: Number next to \( a \): \( -7 \)
• Constant Terms: Terms without a variable: \( -1, 16 \)

Example 3: \( 9 - 6k + 8k + 1 \)

• Variable Terms: Terms with \( k \): \( -6k, 8k \)
• Coefficients: Numbers next to \( k \): \( -6, 8 \)
• Constant Terms: Terms without a variable: \( 9, 1 \)

Example 4: \( r - 14 - 5 + 2r \)

• Variable Terms: Terms with \( r \): \( r, 2r \) (Note: \( r \) has an implicit coefficient of \( 1 \))
• Coefficients: Numbers next to \( r \): \( 1, 2 \)
• Constant Terms: Terms without a variable: \( -14, -5 \)

Example 5: \( -6 + 7w - w - 13 \)

• Variable Terms: Terms with \( w \): \( 7w, -w \) (Note: \( -w \) has an implicit coefficient of \( -1 \))
• Coefficients: Numbers next to \( w \): \( 7, -1 \)
• Constant Terms: Terms without a variable: \( -6, -13 \)

Example 6: \( \frac{1}{2}p + 14 - 2 - 9p \)

• Variable Terms: Terms with \( p \): \( \frac{1}{2}p, -9p \)
• Coefficients: Numbers next to \( p \): \( \frac{1}{2}, -9 \)
• Constant Terms: Terms without a variable: \( 14, -2 \)

Example 7: \( 8x + 3y + 15y \)

• Variable Terms: Terms with \( x \) or \( y \): \( 8x, 3y, 15y \)
• Coefficients: Numbers next to variables: \( 8 \) (for \( x \)), \( 3, 15 \) (for \( y \))
• Constant Terms: No constant terms (all terms have variables)

Example 8: \( -3m + 7n - 14 + 8m \)

• Variable Terms: Terms with \( m \) or \( n \): \( -3m, 7n, 8m \)
• Coefficients: Numbers next to variables: \( -3, 8 \) (for \( m \)), \( 7 \) (for \( n \))
• Constant Terms: Term without a variable: \( -14 \)

Example 9: \( -7w + 2u - 11 - 4 + 6w \)

• Variable Terms: Terms with \( w \) or \( u \): \( -7w, 2u, 6w \)
• Coefficients: Numbers next to variables: \( -7, 6 \) (for \( w \)), \( 2 \) (for \( u \))
• Constant Terms: Terms without a variable: \( -11, -4 \)

Example 10: \( \frac{2}{3}p - \frac{5}{6}q + \frac{1}{4} \)

• Variable Terms: Terms with \( p \) or \( q \): \( \frac{2}{3}p, -\frac{5}{6}q \)
• Coefficients: Numbers next to variables: \( \frac{2}{3} \) (for \( p \)), \( -\frac{5}{6} \) (for \( q \))
• Constant Terms: Term without a variable: \( \frac{1}{4} \)

Final Table (Filled):

Example	Expression	Variable Terms	Coefficients	Constant Terms
2	\( -7a - 1 + 16 \)	\( -7a \)	\( -7 \)	\( -1, 16 \)
3	\( 9 - 6k + 8k + 1 \)	\( -6k, 8k \)	\( -6, 8 \)	\( 9, 1 \)
4	\( r - 14 - 5 + 2r \)	\( r, 2r \)	\( 1, 2 \)	\( -14, -5 \)
5	\( -6 + 7w - w - 13 \)	\( 7w, -w \)	\( 7, -1 \)	\( -6, -13 \)
6	\( \frac{1}{2}p + 14 - 2 - 9p \)	\( \frac{1}{2}p, -9p \)	\( \frac{1}{2}, -9 \)	\( 14, -2 \)
7	\( 8x + 3y + 15y \)	\( 8x, 3y, 15y \)	\( 8, 3, 15 \)	None
8	\( -3m + 7n - 14 + 8m \)	\( -3m, 7n, 8m \)	\( -3, 7, 8 \)	\( -14 \)
9	\( -7w + 2u - 11 - 4 + 6w \)	\( -7w, 2u, 6w \)	\( -7, 2, 6 \)	\( -11, -4 \)
10	\( \frac{2}{3}p - \frac{5}{6}q + \frac{1}{4} \)	\( \frac{2}{3}p, -\frac{5}{6}q \)	\( \frac{2}{3}, -\frac{5}{6} \)	\( \frac{1}{4} \)