Question

2)
a) what value of x will make the expression $6(x + 4) - 3(x - 2)$ equal to 30 ?
b) -30 ?

Explanation:

Part (a)

Step 1: Expand the expression

First, we expand \(6(x + 4)-3(x - 2)\) using the distributive property (\(a(b + c)=ab+ac\)).
\[

$$\begin{align*} 6(x + 4)-3(x - 2)&=6x+24-(3x - 6)\\ &=6x + 24-3x + 6 \end{align*}$$

\]

Step 2: Combine like terms

Combine the \(x\)-terms and the constant terms.
\[

$$\begin{align*} 6x-3x+24 + 6&=(6x-3x)+(24 + 6)\\ &=3x+30 \end{align*}$$

\]

Step 3: Set the equation and solve for \(x\)

We want \(3x + 30=30\). Subtract 30 from both sides:
\[

$$\begin{align*} 3x+30-30&=30-30\\ 3x&=0 \end{align*}$$

\]
Divide both sides by 3:
\[
x = 0
\]

Part (b)

Step 1: Use the simplified expression

From part (a), we know the expression simplifies to \(3x + 30\). We want \(3x+30=-30\).

Step 2: Solve for \(x\)

Subtract 30 from both sides:
\[

$$\begin{align*} 3x+30-30&=-30-30\\ 3x&=-60 \end{align*}$$

\]
Divide both sides by 3:
\[
x=-20
\]

Answer:

a) \(x = 0\)

b) \(x=-20\)