Question

a) what value of x will make the expression $7x + 3(x - 5)$ equal to 75?
b) what value of x will make the expression $7x + 3(x - 5)$ equal to -75?

Explanation:

Part (a)

Step 1: Set up the equation

We set the expression \(7x + 3(x - 5)\) equal to \(75\), so we have the equation:
\[7x + 3(x - 5)=75\]

Step 2: Distribute the 3

Using the distributive property \(a(b - c)=ab - ac\), we get:
\[7x+3x - 15 = 75\]

Step 3: Combine like terms

Combine the \(x\) terms: \(7x+3x = 10x\), so the equation becomes:
\[10x-15 = 75\]

Step 4: Add 15 to both sides

To isolate the term with \(x\), we add \(15\) to both sides:
\[10x-15 + 15=75 + 15\]
\[10x=90\]

Step 5: Divide by 10

Divide both sides by \(10\) to solve for \(x\):
\[x=\frac{90}{10}=9\]

Part (b)

Step 1: Set up the equation

We set the expression \(7x + 3(x - 5)\) equal to \(-75\), so we have the equation:
\[7x + 3(x - 5)=-75\]

Step 2: Distribute the 3

Using the distributive property \(a(b - c)=ab - ac\), we get:
\[7x+3x - 15=-75\]

Step 3: Combine like terms

Combine the \(x\) terms: \(7x + 3x=10x\), so the equation becomes:
\[10x-15=-75\]

Step 4: Add 15 to both sides

To isolate the term with \(x\), we add \(15\) to both sides:
\[10x-15 + 15=-75 + 15\]
\[10x=-60\]

Step 5: Divide by 10

Divide both sides by \(10\) to solve for \(x\):
\[x=\frac{-60}{10}=-6\]

Answer:

s:
a) \(x = 9\)

b) \(x=-6\)