QuestionClassify the equation $4(x-6)+5x=5x+4(x-6)$ as conditional, identity, or contradiction.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $4(x-6)+5 x=5 x+4(x-6)$ . We need to determine if this equation is a conditional equation, an identity, or a contradiction.

STEP 2

First, we need to simplify both sides of the equation. Let's start with the left side of the equation.
$4(x-6)+5 x =4x -24 +5x$

STEP 3

Combine like terms on the left side of the equation.
$x -24 +5x =9x -24$

STEP 4

Now, let's simplify the right side of the equation.
$x+4(x-6) =x +4x -24$

STEP 5

Combine like terms on the right side of the equation.
$5x +4x -24 =9x -24$

STEP 6

Now, we have simplified both sides of the equation and we have $9x -24 =9x -24$

STEP 7

Since both sides of the equation are identical, the equation is true for all values of x. Therefore, the equation is an identity.
The equation $4(x-6)+5 x=5 x+4(x-6)$ is an identity.

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