BRAINIEST IF ANSWERED CORRECTLY Create a single variable linear equation that has no solution. Solve the equation algebraically to pro

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BRAINIEST IF ANSWERED CORRECTLY
Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution. Create a single variable linear equation that has one solution. Solve the equation algebraically to prove that there is one distinct solution for the equation. Create a single variable linear equation that has infinitely many solutions. Solve the equation algebraically to prove that there is an infinite number of solutions for the equation

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Calantha 5 years 2021-08-14T23:14:09+00:00 1 Answers 71 views 0

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  1. Ben
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    2021-08-14T23:15:44+00:00
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    An example of something that doesn’t have a solution is something like x+2 = x+3

    If we subtract x from both sides, then we end up with 2 = 3, which is always false.

    No matter what we plug in for x, the original equation will always be false. The right hand side is always 1 larger than the left side. So that’s why we don’t have any solutions here.

    Side note: equations of this form are known as contradictions (or we could say the equation is inconsistent).

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    An example of something that has one solution is 3x+2 = 2x+7

    Solving this equation leads us to…

    3x+2 = 2x+7

    3x-2x = 7-2

    1x = 5

    x = 5

    To verify the solution, we plug it back into the original equation

    3x+2 = 2x+7

    3(5)+2 = 2(5)+7

    15+2 = 10+7

    17 = 17

    We get the same thing on both sides, so we get a true statement. This confirms that x = 5 is the solution to 3x+2 = 2x+7.

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    An example of an equation with infinitely many solutions is 2x+4 = 2(x+2)

    Notice how both sides are the same thing. The 2(x+2) distributes out to get 2x+4

    Since we have the exact same identical expression on both sides, this ultimately means no matter what we plug in for x, we’ll get a true statement. True statements (like the conclusion at the last section) are simply anything with the same number on both sides after simplifying everything.

    Side note: equations of this form are known as identities

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )