Which expression is equivalent to 2/3 x + 1?
Responses
1/3 (2x + 3)
2/3 (2x + 3)
2/3 (3x + 2)
2/3 (3x + 1)
1/3 (2x + 3)
To find the equivalent expression, we need to simplify the given expression.
The given expression is 2/3 x + 1.
We can distribute the 2/3 to both terms inside the parentheses:
2/3 x + 2/3(1)
Simplifying, we get:
2/3 x + 2/3
Combining like terms, we get:
(2/3 x + 2/3)
Now, to determine which response option is equivalent, we compare it to the simplified expression:
1/3 (2x + 3)
2/3 (2x + 3)
2/3 (3x + 2)
2/3 (3x + 1)
Out of the given options, the expression that is equivalent to 2/3 x + 1 is:
2/3 (3x + 1)
To determine which expression is equivalent to 2/3 x + 1, you need to simplify the given expressions by distributing the fraction 2/3 to the terms inside the parentheses.
Let's evaluate each expression:
1) 1/3 (2x + 3)
To simplify this expression, distribute 1/3 to the terms inside the parentheses:
1/3 * 2x = 2/3x
1/3 * 3 = 1
Simplified expression: 2/3x + 1
2) 2/3 (2x + 3)
Again, distribute 2/3 to the terms inside the parentheses:
2/3 * 2x = 4/3x
2/3 * 3 = 2
Simplified expression: 4/3x + 2
3) 2/3 (3x + 2)
Distributing 2/3 to the terms inside the parentheses:
2/3 * 3x = 6/3x = 2x
2/3 * 2 = 4/3
Simplified expression: 2x + 4/3
4) 2/3 (3x + 1)
Distributing 2/3 to the terms inside the parentheses:
2/3 * 3x = 6/3x = 2x
2/3 * 1 = 2/3
Simplified expression: 2x + 2/3
Comparing these simplified expressions to 2/3 x + 1, the equivalent expression is option 4) 2/3 (3x + 1).