Question

1. 4y - 7x - 12y + 3x
2. 4(6 - x) + 3(x - 8)

Explanation:

Problem 22: \(4y - 7x - 12y + 3x\)

Step 1: Group like terms

Group the \(x\)-terms and \(y\)-terms together: \((4y - 12y)+(-7x + 3x)\)

Step 2: Combine like terms

For \(y\)-terms: \(4y - 12y = -8y\)
For \(x\)-terms: \(-7x + 3x = -4x\)
So the simplified expression is \(-8y - 4x\) (or can be written as \(-4x - 8y\))

Step 1: Distribute the coefficients

Distribute 4 into \((6 - x)\) and 3 into \((x - 8)\):
\(4\times6 - 4\times x+3\times x - 3\times8\)
Which simplifies to: \(24 - 4x + 3x - 24\)

Step 2: Combine like terms

Combine the constant terms: \(24 - 24 = 0\)
Combine the \(x\)-terms: \(-4x + 3x = -x\)
So the simplified expression is \(-x\)

Answer:

\(-8y - 4x\) (or \(-4x - 8y\))

Problem 25: \(4(6 - x)+3(x - 8)\)