Question

1. $-5(y + 10)$
2. write $3x - 1 + 5x + 7$ in simplest form.
3. find $(x + 1) + (x + 1)$.
4. find $(4x - 7) - (2x - 2)$

Explanation:

Problem 9: Simplify \(-5(y + 10)\)

Step 1: Apply the distributive property

The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = - 5\), \(b=y\) and \(c = 10\). So we have \(-5\times y+(-5)\times10\).

Step 2: Calculate the products

\(-5\times y=-5y\) and \(-5\times10 = - 50\). So the simplified form is \(-5y-50\).

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

The \(x\)-terms are \(3x\) and \(5x\). Combining them, we get \(3x + 5x=8x\).

Step 2: Combine the constant terms

The constant terms are \(-1\) and \(7\). Combining them, we get \(-1 + 7 = 6\).

Step 3: Combine the results from Step 1 and Step 2

Putting the combined \(x\)-terms and the combined constant terms together, we have \(8x+6\).

Step 1: Remove the parentheses

Since there are no coefficients outside the parentheses (other than \(1\)), we can remove them: \(x + 1+x + 1\).

Step 2: Combine like terms (the \(x\)-terms)

The \(x\)-terms are \(x\) and \(x\). Combining them, we get \(x+x = 2x\).

Step 3: Combine the constant terms

The constant terms are \(1\) and \(1\). Combining them, we get \(1 + 1=2\).

Step 4: Combine the results from Step 2 and Step 3

Putting the combined \(x\)-terms and the combined constant terms together, we have \(2x+2\).

Answer:

\(-5y - 50\)

Problem 10: Simplify \(3x-1 + 5x+7\)