SOLUTION: I need help solving the radical equation 2x+3-x+1=1

Question 121846: I need help solving the radical equation
2x+3-x+1=1
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Several rules for solving equations such as these are:
.
(1) Combine like terms on both sides
(2) Get the numbers on one side and the unknown variable terms on the other
(3) Combine terms again after they are collected on one side
(4) Divide by the multiplier of the unknown to solve
.
Let's apply these rules to the given problem. You were given:
.
2x + 3 - x + 1 = 1
.
Let's apply rule (1) by combining like terms on the left side. Note the +3 and the +1 are like
terms and they add to give +4. Notice also that the 2x and -x are like terms and they combine
to +x. There is only a single term on the right side of the equation, so no combining is
needed on that side. So after applying rule (1) we are left with:
.
x + 4 = 1
.
Next apply rule (2). The variable term (in this problem it is x) is on the left side, but the
left side also has the constant 4. We need to get the +4 on the other side of the equation
so that it is not on the same side of the equal sign as the 1. You can do this by subtracting
+4 from both sides to get:
.
x + 4 - 4 = 1 - 4
.
Now apply rule (3) and combine the constants on both side. On the left side the +4 and the -4
combine to cancel each other out. So they drop from the equation. On the right side the +1
and the -4 combine to give -3. As a result of this combining the equation is reduced to:
.
x = -3
.
Finally, you apply rule (4). But in this problem the multiplier of x is just +1 and dividing
both sides of the equation by +1 changes nothing. So you have solved the problem, and the
answer you got was x = -3
.
You can check this problem by returning to the original equation you were given and substituting
-3 for x to see if both sides of the equation are equal. The original equation was:
.
2x + 3 - x + 1 = 1
.
Putting -3 in for x results in:
.
2(-3) + 3 - (-3) + 1 = 1
.
This reduces to:
.
-6 + 3 + 3 + 1 = 1
.
If you algebraically add the numbers on the left side, the equation becomes:
.
1 = 1
.
And since this balances, we have the correct answer of x = -3.
.
Hope this helps you to understand some fundamental processes of solving equations.
.
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