Simplify the algebraic expression 4(3x + 5) - 15.

Step-by-step solution

1. 1

   Respect the order of operations: the bracket is multiplied, not added, so distribute first. The $-15$ sits outside the product and cannot be combined with anything until the parentheses are gone. Trying to compute $5-15$ first would be an order-of-operations error.

2. 2

   Distribute the $4$ over both terms.

   $4(3x+5)=4\cdot3x+4\cdot5=12x+20$

   Multiplying only the first term — writing $12x+5$ at this stage — is the most common slip.

3. 3

   Rewrite the whole expression.

   $12x+20-15$

4. 4

   Combine only the like terms. $20$ and $-15$ are both constants, so they combine to $5$. The term $12x$ has no partner, so it is carried through unchanged:

   $12x+5$

5. 5

   Check by substitution. At $x=0$: original $=4(5)-15=5$, simplified $=5$ ✓. At $x=1$: $4(8)-15=17$ and $12+5=17$ ✓. At $x=-2$: $4(-6+5)-15=-4-15=-19$ and $-24+5=-19$ ✓.