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QuestionSolve 2x+17=32x + 17 = 3. Is it an identity, contradiction, or what is the solution set? A, B, or C?

Studdy Solution

STEP 1

Assumptions1. The equation is x+17=3x +17 =3 . We are solving for xx
3. The equation is linear, not quadratic or other forms

STEP 2

We need to isolate xx on one side of the equation. We can start by subtracting17 from both sides of the equation.
2x+17−17=−172x +17 -17 = -17

STEP 3

implify the equation.
2x=3−172x =3 -17

STEP 4

Calculate the right side of the equation.
2x=−142x = -14

STEP 5

Next, we need to isolate xx by dividing both sides of the equation by2.
2x2=−142\frac{2x}{2} = \frac{-14}{2}

STEP 6

implify the equation to find the value of xx.
x=−x = -

STEP 7

Now, we need to check the solution by substituting x=−7x = -7 into the original equation.
2(−7)+17=32(-7) +17 =3

STEP 8

Calculate the left side of the equation.
−14+17=3-14 +17 =3

STEP 9

implify the left side of the equation.
3=33 =3The left side of the equation equals the right side, so x=−7x = -7 is the correct solution.
The solution set is {−7}\{-7\}.

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