QuestionCombine the expressions: $(2x + 5y - z) + (-6x - 4y + 7z) - 4x + 6y + 6z + 4x + y + 6z - 4x - y + 6z$ .

Studdy Solution

STEP 1

Assumptions1. We are given five expressions $( x+5 y-z)$ , $(-6 x-4 y+7 z)$ , $-4 x+6 y+6 z$ 4 x+y+6 z $, and$ -4 x-y+6 z$. . We are to simplify these expressions.

STEP 2

First, we need to simplify the first two expressions by adding them together. We can do this by adding the coefficients of the like terms.
$(2 x+5 y-z)+(-6 x-4 y+7 z) = (2x -6x) + (5y -4y) + (-z +7z)$

STEP 3

implify the expression.
$= -x + y +6z$

STEP 4

Now, we compare this expression with the other given expressions. We see that it matches with the third, fifth and sixth expressions.
$-4x + y +6z = -4 x+6 y+6 z$ $-4x + y +6z = -4 x+y+6 z$ $-4x + y +6z = -4 x-y+6 z$

STEP 5

We see that the first and second expressions are equal to the third, fifth and sixth expressions. Therefore, we can say that all the given expressions are equal.
$-4x + y +z = -4 x+ y+ z = -4 x+y+ z = -4 x-y+ z$

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