Question

⑱ -9x - y + 1 + 5y + 3x - 10
⑲ -x + 8 + 6x - 4y - 8x + 3
⑳ 4x - 7 + y - 7x - (-3y)
㉑ 8x - 5y - x + 9 - y

Explanation:

To solve these algebraic expression simplification problems, we will combine like terms (terms with the same variable or constant terms) for each expression. Let's solve each one step by step:

Problem 19: \(-x + 8 + 6x - 4y - 8x + 3\)

Step 1: Identify and group like terms

• For \(x\)-terms: \(-x + 6x - 8x\)
• For \(y\)-terms: \(-4y\)
• For constant terms: \(8 + 3\)

Step 2: Combine \(x\)-terms

\(-x + 6x - 8x = (-1 + 6 - 8)x = (-3)x = -3x\)

Step 3: Combine constant terms

\(8 + 3 = 11\)

Step 4: Write the simplified expression

Combine all terms: \(-3x - 4y + 11\)

Problem 20: \(4x - 7 + y - 7x - (-3y)\)

First, simplify the double negative: \(-(-3y) = +3y\)

Step 1: Identify and group like terms

• For \(x\)-terms: \(4x - 7x\)
• For \(y\)-terms: \(y + 3y\)
• For constant terms: \(-7\)

Step 2: Combine \(x\)-terms

\(4x - 7x = (4 - 7)x = -3x\)

Step 3: Combine \(y\)-terms

\(y + 3y = (1 + 3)y = 4y\)

Step 4: Write the simplified expression

Combine all terms: \(-3x + 4y - 7\)

Problem 21: \(8x - 5y - x + 9 - y\)

Step 1: Identify and group like terms

• For \(x\)-terms: \(8x - x\)
• For \(y\)-terms: \(-5y - y\)
• For constant terms: \(9\)

Step 2: Combine \(x\)-terms

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

Step 3: Combine \(y\)-terms

\(-5y - y = (-5 - 1)y = -6y\)

Step 4: Write the simplified expression

Combine all terms: \(7x - 6y + 9\)

Final Answers:

1. \(\boldsymbol{-3x - 4y + 11}\)
2. \(\boldsymbol{-3x + 4y - 7}\)
3. \(\boldsymbol{7x - 6y + 9}\)

(Note: Problem 18 is partially visible; if you need help with it, please share the full expression!)

Answer:

To solve these algebraic expression simplification problems, we will combine like terms (terms with the same variable or constant terms) for each expression. Let's solve each one step by step:

Problem 19: \(-x + 8 + 6x - 4y - 8x + 3\)

Step 1: Identify and group like terms

• For \(x\)-terms: \(-x + 6x - 8x\)
• For \(y\)-terms: \(-4y\)
• For constant terms: \(8 + 3\)

Step 2: Combine \(x\)-terms

\(-x + 6x - 8x = (-1 + 6 - 8)x = (-3)x = -3x\)

Step 3: Combine constant terms

\(8 + 3 = 11\)

Step 4: Write the simplified expression

Combine all terms: \(-3x - 4y + 11\)

Problem 20: \(4x - 7 + y - 7x - (-3y)\)

First, simplify the double negative: \(-(-3y) = +3y\)

Step 1: Identify and group like terms

• For \(x\)-terms: \(4x - 7x\)
• For \(y\)-terms: \(y + 3y\)
• For constant terms: \(-7\)

Step 2: Combine \(x\)-terms

\(4x - 7x = (4 - 7)x = -3x\)

Step 3: Combine \(y\)-terms

\(y + 3y = (1 + 3)y = 4y\)

Step 4: Write the simplified expression

Combine all terms: \(-3x + 4y - 7\)

Problem 21: \(8x - 5y - x + 9 - y\)

Step 1: Identify and group like terms

• For \(x\)-terms: \(8x - x\)
• For \(y\)-terms: \(-5y - y\)
• For constant terms: \(9\)

Step 2: Combine \(x\)-terms

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

Step 3: Combine \(y\)-terms

\(-5y - y = (-5 - 1)y = -6y\)

Step 4: Write the simplified expression

Combine all terms: \(7x - 6y + 9\)

Final Answers:

1. \(\boldsymbol{-3x - 4y + 11}\)
2. \(\boldsymbol{-3x + 4y - 7}\)
3. \(\boldsymbol{7x - 6y + 9}\)

(Note: Problem 18 is partially visible; if you need help with it, please share the full expression!)