Question

which of these equations have identical expressions on each side of the equal sign? select two that apply. a $x + 4 = x + 4$ b $6 + x = 6 - x$ c $2x = 2 + x$ d $5x = 5x$

Explanation:

Step1: Analyze Option A

The left - hand side (LHS) of the equation in option A is \(x + 4\) and the right - hand side (RHS) is also \(x+4\). So, the expressions on both sides of the equal sign are identical.

Step2: Analyze Option B

The LHS of the equation in option B is \(6 + x\) and the RHS is \(6 - x\). Since \(x\) and \(-x\) are not the same (unless \(x = 0\), but we are looking at the expressions themselves, not their values for specific \(x\)), the expressions on both sides are not identical.

Step3: Analyze Option C

The LHS of the equation in option C is \(2x\) and the RHS is \(2 + x\). \(2x\) and \(2 + x\) are different expressions (for example, if \(x=3\), \(2x = 6\) and \(2 + x=5\)). So, the expressions on both sides are not identical.

Step4: Analyze Option D

The LHS of the equation in option D is \(5x\) and the RHS is also \(5x\). So, the expressions on both sides of the equal sign are identical.

Answer:

A. \(x + 4 = x + 4\), D. \(5x = 5x\)