in the equation 6x - 2 = -4x + 2, spencer claims that the first step is to add 4x to both sides. jeremiah…

in the equation 6x - 2 = -4x + 2, spencer claims that the first step is to add 4x to both sides. jeremiah claims that the first step is to subtract 6x from both sides. who is correct? explain.

in the equation 6x - 2 = -4x + 2, spencer claims that the first step is to add 4x to both sides. jeremiah claims that the first step is to subtract 6x from both sides. who is correct? explain.

Answer

Explanation:

Step1: Recall equation - solving principle

The goal is to isolate the variable. Adding or subtracting the same quantity from both sides of an equation keeps it balanced.

Step2: Analyze Spencer's claim

Adding (4x) to both sides of (6x - 2=-4x + 2) gives ((6x+4x)-2=(-4x + 4x)+2), simplifies to (10x-2 = 2), moving (x) - terms to one side.

Step3: Analyze Jeremiah's claim

Subtracting (6x) from both sides of (6x - 2=-4x + 2) gives ((6x-6x)-2=(-4x-6x)+2), simplifies to (-2=-10x + 2), also moving (x) - terms to one side.

Answer:

Both Spencer and Jeremiah are correct. When solving the equation (6x - 2=-4x + 2), adding (4x) to both sides or subtracting (6x) from both sides are valid first - steps as they both aim to isolate the variable (x) by getting all (x) - terms on one side of the equation.