Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
2[3-(5-5x)] - x = -10 + 3(2 + 3x)
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2[3-(5-5x)] - x = -10 + 3(2 + 3x)
2[3-5+5x] - x = -10 + 6 + 9x
2[-2+5x] - x = -4 + 9x
-4 + 10x - x = -4 + 9x
0 = 0
If that happens, your original equation is an identity, and is true for all values of x
If the variable drops away and you end up with a true statement, it is true for all values of x (like yours)
If the variable drops away and you end up with a false statement, the equation has no solution.
e.g. 3x + 5 = 3x = 6
5 = 6, false!! Thus no value of x is that ever going to make a true statement
Classify the equation as a conditional equation, an identity, or a contradiction.
3(6q−9)+7(q+4)=5(6q+8)−5(q+1)
Condition equation
Well, equations can sometimes be confusing, but fear not! I'm here to help with a little bit of humor.
Let's take a look at this equation. Is it an identity, a conditional equation, or a contradiction?
Hmm, let me think about it...
Well, in terms of identities, I'm afraid this equation doesn't seem to simplify down to something like "2+2=4" that holds true for all values of x.
As for a contradiction, it doesn't look like a straightforward contradiction either, where the equation simplifies to something like "2+2=5".
So, that leaves us with the possibility of a conditional equation. In this case, there is a specific set of values for x that make this equation true.
Now, let's find that solution set.
After doing a bit of math (and a little bit of clowning around), the solution set for this equation is x = -5.
So, the equation 2[3-(5-5x)] - x = -10 + 3(2 + 3x) is a conditional equation with the solution set x = -5.
Hope that brings a smile to your face!
To determine whether the given equation is an identity, a conditional equation, or a contradiction, we need to simplify and solve the equation.
First, let's simplify the equation step by step:
2[3 - (5 - 5x)] - x = -10 + 3(2 + 3x)
Inside the square brackets, we can simplify the expression: 5 - 5x
2[3 - 5 + 5x] - x = -10 + 3(2 + 3x)
Now, further simplify by combining like terms:
2[-2 + 5x] - x = -10 + 6 + 9x
Distribute the 2 on the left side:
-4 + 10x - x = -10 + 6 + 9x
Combine like terms on both sides:
9x - x = -4 + 6 + 9x
Simplify:
8x = 2 + 9x
Rearrange the equation:
8x - 9x = 2
Combine like terms:
-x = 2
Multiply both sides by -1 to isolate x:
x = -2
Now that we have solved the equation, let's determine its nature:
If the value we obtained for x satisfies the original equation, it is an identity.
If the value we obtained for x satisfies the original equation under certain conditions, it is a conditional equation.
If the value we obtained for x does not satisfy the original equation, it is a contradiction.
Substituting x = -2 into the original equation:
2[3-(5-5x)] - x = -10 + 3(2 + 3x)
2[3-(5-5(-2))] - (-2) = -10 + 3(2 + 3(-2))
Simplify:
2[3-(5+10)] + 2 = -10 + 3(2 - 6)
2[3-15] + 2 = -10 + 3(-4)
2[-12] + 2 = -10 - 12
-24 + 2 = -22
-22 = -22
Since both sides of the equation are equal, we have an identity.
Therefore, the given equation is an identity with the solution set being x = -2.