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)