M/J 18/P21/Q3/a,b (a) Solve $$ 4(p-3)=2 p+7 $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 4(p - 3) = 2p + 7 $$, follow these steps:

1. **Expand the Left Side**

Distribute the 4 to both terms inside the parentheses:

$$
   4(p - 3) = 4p - 12
   $$

So, the equation becomes:

$$
   4p - 12 = 2p + 7
   $$

2. **Move All Terms Involving $$ p $$ to One Side**

Subtract $$ 2p $$ from both sides to get all $$ p $$-terms on the left:

$$
   4p - 2p - 12 = 7
   $$
   
   Simplify:

$$
   2p - 12 = 7
   $$

3. **Isolate the $$ p $$-Term**

Add 12 to both sides to isolate the term with $$ p $$:

$$
   2p - 12 + 12 = 7 + 12
   $$
   
   Simplify:

$$
   2p = 19
   $$

4. **Solve for $$ p $$**

Divide both sides by 2:

$$
   p = \frac{19}{2}
   $$
   
   $$
   p = 9.5
   $$

**Final Solution:** $$ p = \frac{19}{2} $$ or $$ p = 9.5 $$
$$ p = \frac{19}{2} $$ or $$ p = 9.5 $$

M/J 18/P21/Q3/a,b (a) Solve \( 4(p-3)=2 p+7 \)