Please help me! 90 points!
1 answer:
To make it so that the equations have no solutions, we have to make the x's cancel out.
Lets do this by changing -5 into 2.
Equation 1;
This works, because when we expand the brackets, we get 2x + 1 on the right side. Then when we subtract 2x from both sides to try and solve the equation, we end up cancelling out all of the x's, leaving us with 3=2. And since 3 does not equal 2, hence there are no solutions
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To make an equation have an infinite amount of solutions, we have to make both sides (the left and right) be exactly the same.
We can do this by changing the 3 in our equation above into 2:
Equation 2:
No matter what we say what x is, both sides of the equation will be the same, and cancel down to 0.
In that equation, x could be 0, or 1 or 2 or 324 or 2041 or any other number (hence any infinite number of solutions)
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Explanation for the equation with only one solution:
It only has one solution, because there is only one value for x that makes the equal sign correct..
-5x + 3 = 2(x + 1)
If we solve it we get that x = 1/7.
If we substitute in 1/7 into x, we get:
-5(1/7) + 3 = 2(1/7 + 1)
-5/7 + 3 = 2/7 +2
16/7 = 16/7 (now the equal sign is correct)
But if we substitute in other number, like 3, the equal sign won't be true.
1/7 is the only number that can be substituted into x to make the equation 'correct'. Hence, there is only one solution
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