Question

unit 4: expressions & properties
per: ____ homework 5: combining like terms
directions: identify the variable terms, constant terms, and coefficients for each expression.

	expression	variable terms	coefficients	constant terms
x	$4x + 15x$
x	$8r + 7 - 2r$
x	$-6n - 25 + 7n - 4$
x	$3a - 4a + 17 + a - 1$
x	$11c - 4d + c - 9d - 2c$
x	$-5x + 3 + 2y - y + 8x - 14$

directions: simplify each expression by combining like terms.

1. $8w + 4w$ \t\t10. $-6c + 4c$
2. $4x - 7x + 28$ \t\t11. $13 + 9p - 20$
3. $7 + \frac{4}{5}a - \frac{2}{3}a + 2$ \t\t12. $12k - 2 - 1 + 2k$
4. $-3n - 2n + 18 + 12n$ \t\t13. $v - 14 + 9v - 5$
5. $20 + 17z - 16z - 12$ \t\t14. $-2 - j + 15 + 8j - 11$
6. $5r + 16s - 7s - 2r + r$ \t\t15. $-n + 8n - 7m + 4n + m$
7. $5x - 9 - 4 + y - 12x$ \t\t16. $-2a + 9 - b - 4b + 7a - 1$

Explanation:

Let's solve some of these problems step by step. We'll start with the "Simplify each expression by combining like terms" section.

Problem 2: \( 8w + 4w \)

Step 1: Identify like terms

Both terms have the variable \( w \), so they are like terms.

Step 2: Combine the coefficients

Add the coefficients of \( w \): \( 8 + 4 = 12 \). So, \( 8w + 4w = 12w \).

Step 1: Combine like terms (the \( x \)-terms)

Subtract the coefficients of \( x \): \( 4 - 7 = -3 \). So, \( 4x - 7x = -3x \).

Step 2: Write the simplified expression

The constant term \( 28 \) remains. So, \( 4x - 7x + 28 = -3x + 28 \).

Step 1: Combine constant terms

Add \( 7 \) and \( 2 \): \( 7 + 2 = 9 \).

Step 2: Combine the \( a \)-terms

To combine \( \frac{4}{5}a \) and \( -\frac{2}{3}a \), find a common denominator (15).
\( \frac{4}{5}a = \frac{12}{15}a \) and \( -\frac{2}{3}a = -\frac{10}{15}a \).
Subtract: \( \frac{12}{15}a - \frac{10}{15}a = \frac{2}{15}a \).

Step 3: Write the simplified expression

Combine the results: \( 9 + \frac{2}{15}a \) (or \( \frac{2}{15}a + 9 \)).

Answer:

\( 12w \)

Problem 3: \( 4x - 7x + 28 \)