Question

the expression 6x - x + 5 as 6 + 5. are 6x - x + 5 and 6 + 5 equivalent expressions? explain.

Explanation:

Step1: Analyze the first expression

The first expression is \(6x - x + 5\). Combine like terms: \(6x - x=5x\), so it simplifies to \(5x + 5\).

Step2: Analyze the second expression

The second expression is \(6 + 5=11\), which is a constant.

Step3: Compare the two expressions

The first expression \(5x + 5\) has a variable term (\(5x\)) and a constant term (\(5\)), while the second expression \(11\) is just a constant. For the expressions to be equivalent, they must have the same value for all values of \(x\). Let's test with \(x = 0\): first expression is \(5(0)+5 = 5\), second is \(11\) (not equal). With \(x = 1\): first is \(5(1)+5=10\), second is \(11\) (not equal). So they are not equivalent.

Answer:

The expressions \(6x - x + 5\) (simplifies to \(5x + 5\)) and \(6 + 5=11\) are not equivalent. The first has a variable term (\(5x\)) and a constant, the second is a constant, and they don't have the same value for all \(x\).