Math Practice U2 L5

Question

Unit 2 All Lessons: Math Practice links
Live Lesson Recording Link *Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
Function of the Day: 3 ( 푤 − 3 ) + 3 7 = 3
What do you know? 1. 6. 2. 7. 3. 8. 4. 9.
5. 10.
Vocabulary Terms - Define/Illustrate 1. Terms 2. Factors 5 Problems - SHOW ALL WORK! 1. 8k – 15 = 4k + 13 2. 2(5 – 3r) = -4r – 16 3. j – (5 – 3j) = 7j + 4 4. 5.
Find any mistakes.
What do I need help with?

Answer 1

Based on the information you provided, it seems like you're working on a math practice assignment in a class. Here's how we can break down and address each section of your assignment:

Function of the Day

For the function of the day, you wrote: \[ 3(w - 3) + 3 = 7 \]

To check if this is true, let's solve for \( w \):

1. Distribute the \( 3 \): \[ 3w - 9 + 3 = 7 \]
2. Simplify: \[ 3w - 6 = 7 \]
3. Add \( 6 \) to both sides: \[ 3w = 13 \]
4. Divide by \( 3 \): \[ w = \frac{13}{3} \approx 4.33 \]

Thus, the function equals \( 7 \) when \( w \) is \( \frac{13}{3} \).

Vocabulary Terms

1. Terms: A term is a single mathematical expression. It could be a number, a variable, or a combination of both multiplied together, such as \( 3x \) or \( -4 \).

   • Illustration: \( 3x + 5y - 7 \) consists of three terms: \( 3x \), \( 5y \), and \(-7\).

2. Factors: Factors are numbers or expressions that can be multiplied together to get another number or expression. For example, in \( 12 \), the factors are \( 1, 2, 3, 4, 6, \) and \( 12 \).

   • Illustration: For the expression \( x^2 - 9 \), the factors are \( (x - 3)(x + 3) \).

Problems – Show All Work

1. Problem 1: \( 8k - 15 = 4k + 13 \)

   • Move \( 4k \) to the left side: \[ 8k - 4k - 15 = 13 \]
   • Combine like terms: \[ 4k - 15 = 13 \]
   • Add \( 15 \) to both sides: \[ 4k = 28 \]
   • Divide by \( 4 \): \[ k = 7 \]

2. Problem 2: \( 2(5 - 3r) = -4r - 16 \)

   • Distribute \( 2 \): \[ 10 - 6r = -4r - 16 \]
   • Move \( 6r \) to the right side: \[ 10 = 2r - 16 \]
   • Add \( 16 \): \[ 26 = 2r \]
   • Divide by \( 2 \): \[ r = 13 \]

3. Problem 3: \( j - (5 - 3j) = 7j + 4 \)

   • Distribute the negative: \[ j - 5 + 3j = 7j + 4 \]
   • Combine like terms: \[ 4j - 5 = 7j + 4 \]
   • Move \( 7j \) to the left: \[ 4j - 7j = 4 + 5 \]
   • Combine like terms: \[ -3j = 9 \]
   • Divide by \( -3 \): \[ j = -3 \]

Find Any Mistakes

• When solving each problem, ensure each step logically follows from the previous one, and watch for signs when moving terms across the equals sign.

What Do I Need Help With?

If there are specific areas of math, such as solving equations, understanding vocabulary, or if you're having trouble with any of the problems, please specify and I'll do my best to help you!

Feel free to ask me for additional clarification or assistance on these topics!