What is it? It is a multistep linear equation. It can be solved in 3 steps, the exact nature of which can be somewhat flexible.
In the most general case, you can subtract one side of the equation from both sides. I like to add the opposite of (subtract) the side with the most-negative or least coefficient of the variable. Here, that's the right side, where the coefficient is -14, which is less than -2.
-2x -10 +14x +7 = 0 . . . . . subtract the right side (actually, add 14x+7)
12x -3 = 0 . . . . . . . . . . . . simplify
x -3/12 = 0 . . . . . . . . . . . . divide by the x-coefficient
x = 3/12 = 1/4 . . . . . . . . . . add the opposite of the constant, reduce the fraction
The value of x that makes this equation true is 1/4.
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A more-often seen approach is to consolidate the variable terms on one side of the equal sign, and consolidate the constant terms on the other side. Then divide by the coefficient of the variable. Here, that looks like ....
... 12x -10 = -7 . . . . . add 14x
... 12x = 3 . . . . . . . . add 10
... x = 3/12 = 1/4 . . . divide by 12
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In any case, you make use of the addition property of equality that lets you <em>add the same thing to both sides of the equation</em>. And, you make use of the multiplication (or division) property of equality that lets you <em>multiply (or divide) both sides of the equation by the same thing</em>. Here, when we say "add ___", we mean "add ___ to both sides of the equation." That's the only way the equal sign remains valid. The same is true for any other operation you may wish to perform: you must do it to both sides of the equation.
