which algebraic expression is equivalent to the expression below?

Question

2.1x+3.5y
given:
0.7(3x-5y)
0.7(3x+5y)
0.7(5x-3y)
0.7(5x+3y)

Answer 1

To find an equivalent algebraic expression to \(2.1x + 3.5y\) from the given options, we can first simplify \(2.1x + 3.5y\).

We can factor out \(0.7\) from \(2.1\) and \(3.5\):

\[ 2.1 = 0.7 \times 3 \] \[ 3.5 = 0.7 \times 5 \]

The expression \(2.1x + 3.5y\) can then be rewritten as:

\[ 2.1x + 3.5y = 0.7(3x + 5y) \]

Now let's check this against the options provided:

1. \(0.7(3x - 5y)\)
2. \(0.7(3x + 5y)\)
3. \(0.7(5x - 3y)\)
4. \(0.7(5x + 3y)\)

The expression \(0.7(3x + 5y)\) matches our derived expression. Therefore, the equivalent algebraic expression is:

\[ \boxed{0.7(3x + 5y)} \]