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Chapter 5: Problem 1

In each case, simplify the given expression, if possible. \(3 x-2 y+7 x-11 y\)

Short Answer

Expert verified
Question: Simplify the following algebraic expression: \(3x-2y+7x-11y\). Answer: The simplified expression is \(10x - 13y\).

Step by step solution

01

Identify like terms

In the given expression, \(3x-2y+7x-11y\), we can identify two pairs of like terms: \(3x\) and \(7x\) (both x terms), and \(-2y\) and \(-11y\) (both y terms).
02

Combine like terms (x terms)

We can start by combining the x terms, \(3x\) and \(7x\). To do this, we add the coefficients (the numbers attached to the variables): \((3+7)x\). This results in \(10x\).
03

Combine like terms (y terms)

Next, we combine the y terms, \(-2y\) and \(-11y\). To do this, we add the coefficients (the numbers attached to the variables): \((-2+-11)y\). This results in \(-13y\).
04

Write the simplified expression

Now that we've combined both pairs of like terms, we can write our simplified algebraic expression by putting the results from Steps 2 and 3 together. This gives us: $$10x - 13y$$

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