Which two statements are correct when simplifying this expression?
12 + 6(3x − 2)
1) The expression can be simplified as 12 + 18x - 12.
2) The expression can be simplified as 18x - 12 + 12.
To simplify the given expression 12 + 6(3x − 2), we need to apply the distributive property.
The distributive property states that when a number is multiplied by a group of terms inside parentheses, we multiply that number with each term inside the parentheses separately.
Step 1: Distribute 6 across the terms inside the parentheses.
6(3x − 2) = 6 * 3x + 6 * (-2)
= 18x - 12
Step 2: Combine like terms.
12 + 18x - 12 = 18x
Now, let's review the statements to determine which two are correct.
Statement 1: The expression simplifies to 18x.
Statement 2: The expression simplifies to 12 + 18x - 12.
Statement 3: The expression simplifies to 12 + 6(3x) - 6(2).
Statement 4: The expression simplifies to 12 + 6(3x − 2).
From the analysis, the correct statements are:
Statement 1: The expression simplifies to 18x.
Statement 4: The expression simplifies to 12 + 6(3x − 2).
To simplify the expression 12 + 6(3x − 2), we can apply the distributive property.
First, let's distribute the 6 to both terms inside the parentheses.
6(3x − 2) becomes 18x − 12.
Now, we replace the original expression with the simplified form:
12 + 18x − 12
Next, we combine like terms. The two -12 terms cancel each other out, leaving us with:
12 + 18x
Finally, the two statements that are correct when simplifying this expression are:
1. The expression 12 + 6(3x − 2) can be simplified as 12 + 18x.
2. The simplified expression 12 + 18x has no like terms to combine further.