Simplify the given algebraic expression: 5(9x - 8) + 12x.

Step-by-step solution

1. 1

   Choose the method: distribute before combining. The $12x$ sits outside the bracket, so it cannot be merged with anything until the bracket is opened. Multiplying $5$ across the bracket is therefore the first move, and the distributive property $a(b+c) = ab + ac$ is what licenses it.

2. 2

   Distribute the 5 across both terms. The $5$ multiplies $9x$ and $-8$ — hitting only the first term is the most common mistake here:

   $5(9x - 8) = 5 \cdot 9x - 5 \cdot 8 = 45x - 40$

3. 3

   Rewrite the whole expression. Put the expanded bracket back with the trailing term:

   $45x - 40 + 12x$

4. 4

   Combine the like terms. $45x$ and $12x$ are like terms because both are a number times $x^1$; the constant $-40$ has no $x$ and stays as it is:

   $45x + 12x - 40 = 57x - 40$

   Writing $57x - 40 = 17x$ by "combining" the $-40$ into the $x$ term is the error to avoid — unlike terms never merge.

5. 5

   Check with a test value. Put $x = 2$ into the original: $5(18-8) + 24 = 5(10) + 24 = 74$. Put $x = 2$ into the answer: $57(2) - 40 = 114 - 40 = 74$ ✓. The two agree, so $57x - 40$ is correct.