Answer:
This has already been answered correctly (x = -2/5), but I'll add the steps required to arrive at that conclusion.
Explanation:
Solving 2(5x+3)=2 requires that we use the order of operations, or PEDMAS, in going through the steps. PEDMAS is the acronym for Parentheses, Exponents, Division, Multiplication, Addition and Subtraction. These are the order in which math operations should be done when solving equations. This provides the "rules of the road" when interpreting how equations were meant to be read.
2(5x+3)=2
1. Parentheses: First, we should complete whatever is inside a set of parentheses, in this case (5x+3). There is nothing we can do with (5x+3) so go to the next step.
2. Exponents: none here, so continue
3. Division: none here, so continue
4. Multiplication: We can do the term 2(5x+3) by multiplying the 2 times each of the values within the parentheses.
2(5x+3) = 10x + 6
We now have:
10x + 6 = 2
5. Addition/Subtraction: Subtract 6 from both sides:
10x + 6 - 6 = 2 - 6
10x = - 4
We've gone through PEDMAS once, so start over again since we are still looking for the value of x.
The only operation left is to divide both sides by 10:
10x = -4
10x/10 = -4/10
x= - 4/10 or -2/5
In general, PEDMAS works quite well. It defines how to interpret the manner in which equations are written. If there is any remaining ambiguity, always work from left to right. Solve the portion on the left first, then move right.
Also, it is always good, and edifying, to try the solution to see if the equation works for that solution. We can ask "Does a value of x=-(2/5) give the answer of "2" when used in 2(5x+3)?
2(5x+3)
2(5*(-2/5) + 3) = 2? for x = -(2/5)
2(5*(-2/5) + 3) = 2?
Use PEDMAS:
2(5*(-0.4) + 3) = 2?
2(-2 + 3) = 2?
2(1) = 2? YES, -(2/5) is correct