Question

the cost of the meat you ordered for the week can be represented by the expression \\(4x + 5 - 2x\\), where \\(x\\) represents the weight of the meat in pounds.

which expression is equivalent to \\(4x + 5 - 2x\\), and why?

• the expression \\(4x + 3x\\) is an equivalent expression as \\(2x\\) is subtracted from \\(5\\) to get the expression.
• the expression \\(2x + 5\\) is equivalent because the like terms are combined to get it.
• the expression \\(9x - 2x\\) is equivalent as the first two terms are added to get the expression.
• the expression \\(7x\\) is equivalent because all three terms are combined to get the expression.

Explanation:

Identify the terms

Identify the terms in the given algebraic expression.
The expression is:

$$4x + 5 - 2x$$

The terms are \(4x\), \(5\), and \(-2x\).

Group like terms

Group the terms that have the same variable and exponent.
The like terms are \(4x\) and \(-2x\).
The constant term is \(5\).

$$(4x - 2x) + 5$$

Combine like terms

Perform the subtraction on the coefficients of the like terms.

$$(4 - 2)x + 5 = 2x + 5$$

Compare with options

Match the simplified expression and reasoning with the choices.

• Option 1 suggests \(4x + 3x\), which is incorrect.
• Option 2 suggests \(2x + 5\) because like terms are combined, which is correct.
• Option 3 suggests \(9x - 2x\), which is incorrect.
• Option 4 suggests \(7x\), which is incorrect.

Answer:

• The expression \(4x + 3x\) is an equivalent expression as \(2x\) is subtracted from 5 to get the expression.
• The expression \(2x + 5\) is equivalent because the like terms are combined to get it. (Correct answer)
• The expression \(9x - 2x\) is equivalent as the first two terms are added to get the expression.
• The expression \(7x\) is equivalent because all three terms are combined to get the expression.