Subtract 3x − 4y − 7z from the sum of x − 3y + 2z and − 4x + 9y − 11z.

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Solution

Let first add the expressions $x - 3 y + 2 z and - 4 x + 9 y - 11 z$ . We get:

$(x - 3 y + 2 z) + (- 4 x + 9 y - 11 z)$
$= x - 3 y + 2 z - 4 x + 9 y - 11 z$
$= x - 4 x - 3 y + 9 y + 2 z - 11 z$ (Collecting like terms)
$= - 3 x + 6 y - 9 z$ (Combining like terms)

Now, subtracting the expression $3 x - 4 y - 7 z$ from the above sum; we get:

$(- 3 x + 6 y - 9 z) - (3 x - 4 y - 7 z) = - 3 x + 6 y - 9 z - 3 x + 4 y + 7 z$
$= - 3 x - 3 x + 6 y + 4 y - 9 z + 7 z$ (Collecting like terms)
$= - 6 x + 10 y - 2 z$ (Combining like terms)

Thus, the answer is $- 6 x + 10 y - 2 z$ .

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