Question

1. a) what value of x will make the expression $6x + 3(x + 4)$ equal to -6 ? b) 48 ?

Explanation:

Part (a)

Step 1: Set up the equation

We set the expression \(6x + 3(x + 4)\) equal to \(-6\), so we have the equation:
\[6x + 3(x + 4)=-6\]

Step 2: Distribute the 3

Using the distributive property \(a(b + c)=ab+ac\), we distribute the 3 in \(3(x + 4)\):
\[6x+3x + 12=-6\]

Step 3: Combine like terms

Combine the \(x\)-terms \(6x\) and \(3x\):
\[9x+12=-6\]

Step 4: Subtract 12 from both sides

Subtract 12 from each side of the equation to isolate the term with \(x\):
\[9x=-6 - 12\]
\[9x=-18\]

Step 5: Divide by 9

Divide both sides by 9 to solve for \(x\):
\[x=\frac{-18}{9}\]
\[x = - 2\]

Step 1: Set up the equation

We set the expression \(6x + 3(x + 4)\) equal to \(48\), so we have the equation:
\[6x + 3(x + 4)=48\]

Step 2: Distribute the 3

Using the distributive property \(a(b + c)=ab + ac\), we distribute the 3 in \(3(x + 4)\):
\[6x+3x + 12=48\]

Step 3: Combine like terms

Combine the \(x\)-terms \(6x\) and \(3x\):
\[9x+12=48\]

Step 4: Subtract 12 from both sides

Subtract 12 from each side of the equation to isolate the term with \(x\):
\[9x=48 - 12\]
\[9x=36\]

Step 5: Divide by 9

Divide both sides by 9 to solve for \(x\):
\[x=\frac{36}{9}\]
\[x = 4\]

Answer:

(a):
\(x=-2\)

Part (b)