Question

11.) $9y + (-15y) = __________$ 12.) $8r + (-7r) = __________$
selected answers to previous page: 5.) 5ab 6.) -2a 9.) -3x

variables with like signs

example 4: $-6y + (-4y) = -10y$ because $-6 + (-4) = -10$

practice: add like terms to simplify using the rules for adding integers with like signs.
1.) $-3x + (-2x) =$ 2.) $-4y + (-y) =$
3.) $-7ab + (-2ab) =$ 4.) $-4x + (-2x) + (-x) =$
5.) $-6z + (-8z) + (-3z) =$ 6.) $-6ab + (-5ab) + (-ab) =$
7.) $-9b + (-4b) + (-3b) =$ 8.) $-8r + -12r + -3r =$

selected answers: 1.) -5x 4.) -7x 7.) -16b

what is the coefficient of “$-y$”?

Explanation:

Problem 11: \( 9y + (-15y) \)

Step 1: Identify like terms

Both terms have the variable \( y \), so they are like terms. We can add their coefficients.
The coefficients are \( 9 \) and \( -15 \).

Step 2: Add the coefficients

\( 9 + (-15) = 9 - 15 = -6 \)

Step 3: Combine with the variable

Multiply the sum of the coefficients by the variable \( y \): \( -6y \)

Step 1: Identify like terms

Both terms have the variable \( r \), so they are like terms. We can add their coefficients.
The coefficients are \( 8 \) and \( -7 \).

Step 2: Add the coefficients

\( 8 + (-7) = 8 - 7 = 1 \)

Step 3: Combine with the variable

Multiply the sum of the coefficients by the variable \( r \): \( 1r = r \) (we can write \( 1r \) as \( r \) since the coefficient \( 1 \) is usually omitted)

Step 1: Identify like terms

Both terms have the variable \( x \), so they are like terms. We can add their coefficients.
The coefficients are \( -3 \) and \( -2 \).

Step 2: Add the coefficients

\( -3 + (-2) = -3 - 2 = -5 \)

Step 3: Combine with the variable

Multiply the sum of the coefficients by the variable \( x \): \( -5x \)

Answer:

\( -6y \)

Problem 12: \( 8r + (-7r) \)