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) \(x=-6\)