Answer:
a = -3
Step-by-step explanation:
This is a linear equation in one variable that has a constant term and a variable term on each side of the equal sign. It can be solved in 3 steps, so can be called a "3-step equation."
The three steps involve separating the variable and constant terms, then dividing by the variable's coefficient.
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-a -10 = 5a +8 . . . . . . given
<h3>step 1</h3>
To separate the variable and constant terms, we eliminate one of the variable terms by adding its opposite to both sides of the equation. It is generally convenient to choose the variable term with the lowest coefficient value. When we add the opposite of that to both sides of the equation, the resulting variable term will have a positive coefficient. (Dealing with positive numbers generally reduces errors.)
Here the two variable terms are -a and 5a. The coefficient -1 is less than the coefficient 5, so we choose to add the opposite of -a to both sides.
-a +a -10 = 5a +a +8 . . . . . add a to both sides
-10 = 6a +8 . . . . . . . . . . . simplify
<h3>step 2</h3>
Now there is only one variable term, but it has a constant added to it. We can eliminate that constant by adding its opposite.
-10 -8 = 6a +8 -8 . . . . . add -8 to both sides
-18 = 6a . . . . . . . . . . . simplify
<h3>step 3</h3>
This equation gives us the value of a multiple of the variable (6a). To get the variable by itself, we multiply by the reciprocal of the variable's coefficient. The product of the coefficient and its reciprocal is 1, so we will have the variable alone.
Multiplying by 1/6 is the same as dividing by 6. Often, it is easier to think in terms of division. However, when the coefficient is a fraction, it can be useful to think in terms of multiplying by the reciprocal of that fraction.
(1/6)(-18) = (1/6)(6a) . . . . . . multiply by 1/6
-3 = a . . . . . . . . . . . . . . . simplify
The solution to the equation is a = -3.
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<em>Additional comment</em>
When we say "add" or "multiply" the equation by some number, we mean that operation to be performed on both sides of the equation. The properties of equality say we can do whatever we like to an equation, as long as we <em>do the same thing to both sides of the equation</em>.
