Which is a reasonable first step that can be used to solve the equation 2(x+6)=3(x-4)+5? combine like terms, 3 and 5, on the right side of the equation. distribute 2 to (x + 6) and 3 to (x – 4). distribute 2 to x on the left side of the equation and 3 to x on the right side of the equation. apply the subtraction property of equality to move the 6 from the left side of the equation to the right side.

  Distribute 2 to (x + 6) and 3 to (x – 4)

Step-by-step explanation:

A good first step for an equation such as this is to eliminate parentheses. That is accomplished by using the distributive property on the left and right. That property requires each term inside parentheses be multiplied by the factor outside parentheses. The process can be described as ...

  Distribute 2 to (x + 6) and 3 to (x – 4)

Comment on further steps

The result of the first step above would be ...

  2x + 12 = 3x - 12 + 5

  19 = x . . . . . . . . . . . next step: add 7-2x to both sides and collect terms

Comment on answer wording

The last answer choice uses the wording "move the 6 from the left side of the equation to the right side". This sort of description is often invoked when a constant needs to be removed from one side of the equation or the other.

  There is no property of equality that supports this action.

If you want to "move" a constant, you can invoke the addition property of equality that lets you add the same number to both sides of the equation. The number you would choose to add is the additive inverse of the one you want to "move."

In the above solution we have the sum -12+5 on the right after the first step. We want to eliminate that sum, so in the next step we show adding the additive inverse of the value of that sum. The sum of -12+5 is -7, and we add 7 to make that sum into the additive identity element, 0. (Likewise, we add -2x to turn the term 2x into the additive identity element, 0.) After these additions, we have ...

  2x -2x +12 +7 = 3x -2x -12 +5 +7

  0 + 19 = x + 0

  19 = x

The relevant property of equality is the addition property of equality, which says I can add the same amount to both sides of the equation. I can't "move" anything without violating the equal sign, but I can use the addition and multiplication properties of equality to do the same thing to both sides of the equation.

both equations and proportions are better.