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How much smaller is $5x - 8y + 9z$ than $12x - 10y - 3z + 16?$

Last updated date: 21st Jul 2024
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Hint: As we know that when we combine numbers and variables in a valid way, using the operations such as addition, subtraction, multiplication, division, exponentiation and other operations and functions then the resulting combination of mathematical symbols is called a mathematical expression. These are also called the fundamental operations. Here we have been given a mathematical expression with the term “ than ” which means to subtract in this case, from the later term.

Complete step-by-step answer:
Here we have to by how much does $5x - 8y + 9z$ than $12x - 10y - 3z + 16$
We simply have to find the difference here. So we will write the above as
$12x - 10y - 3z + 16 - (5x - 8y + 9z)$.
When we break the bracket the sign changes i.e.
$12x - 10y - 3z + 16 - 5x + 8y - 9z + 16$.
We will group the similar terms together and then we subtract it:
$12x - 5x - 10y + 8y - 3z - 9z + 16$.
After subtraction it gives us value $7x - 2y - 12z + 16$
Hence the required answer is $7x - 2y - 12z + 16$.
So, the correct answer is “$7x - 2y - 12z + 16$”.

Note: We should keep in mind that for problems like this, it is good to break up the information and visualize how it fits in together. It should be noted that a mathematical expression does not involve any equal sign as it is an expression. We equal signs $\left( = \right)$ in mathematical equations not in expressions. We should also note that the above given equations are linear equations in three variables. An equation for a straight line is called a linear equation. The standard form of linear equations in two variables is $Ax + By + Cz = R$ .