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1. 5X - 20 = 2(3X - 10) 2. 4X - 16 - 2X = 2(X-8)
3. 6X - 15 = 3(2x - 6) 4. 5X -3(X -4) = 2(X - 6)
Do you know what identits and contradictions are in mathematic terms?
0.0 lets see
An identity is when the equation is true, such as 3 = 1 + 2. A contradiction is when the equation is not true, such as 3 = 4 x 1. If you simplify the equations given, you should be able to solve whether or not they are identities or contradictions
1. 5X - 20 = 2(3X - 10) If we simplify the second half, we will be able to solve the problem. The only step we need to do with this one is distribute, so we just multiply that which is in the parenthesis by the number outside, in this case 2. 1. 5x - 20 = 6x - 20 is the simplified version for the first problem
As we can see, 5x - 20 does not equal 6x - 20, so that would be a contradiction
2. 4X - 16 - 2X = 2(X-8) 4x and -2x are like terms, so we can combine them together to create 2x. 2. 2x - 16 = 2(x - 8) when we use the distributive property, we can simplify the second half to 2. 2x - 16 = 2x - 16 So is this an identity or a contradiction
oh my bad i was doing some thing :(
so 2. is a contradiction
cause the sides are the same yet they're opposite
wait is 2. identity
Yes, 2. is an identity. Are you starting to get the hang of it?
ya, I just saw the question wrong
can you help me with the others?
thanks i'll give you a medal after
3. 6X - 15 = 3(2x - 6) this is just a one step distributive, so the second half will be 6x - 15 = 6x - 18 Identity or contradiction? 4. 5X -3(X -4) = 2(X - 6) This one is more complicated, as there are parentheses on both sides. We just need to tackle them one at a time. The first half will come out as 5x - 3x - 12, and then we can combine the like terms (5x and 3x) so that the first half will be 2x - 12 The second half is just distribution, so 2x - 12. The equation ends up simplifying to 2x - 12 = 2x - 12 Identity or contradiction? Hope I helped!
3. is Identity
sorry I meant for 4
4. is identity and 3. is...
3. is contradiction or neither?
3. is a contradiction. Good job!