QuestionClassify the equation $3(x-2)=4(7-2 x)+11 x$ as conditional, identity, or contradiction.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $3(x-)=4(7-x)+11x$ . . We need to determine if this equation is a conditional equation, an identity, or a contradiction.

STEP 2

First, let's simplify both sides of the equation.On the left side, distribute the to both terms inside the parentheses $(x-2) =x -6$ On the right side, distribute the4 to both terms inside the parentheses and then combine like terms $4(7-2x)+11x =28 -8x +11x =28 +x$

STEP 3

Now, let's rewrite the original equation with the simplified expressions $3x -6 =28 +3x$

STEP 4

Next, let's try to isolate x by subtracting3x from both sides of the equation $3x -3x -6 =28 +3x -3x$ This simplifies to $-6 =28$

STEP 5

The equation $- =28$ is not true for any value of x, so the original equation is a contradiction.
The equation is a contradiction.

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