Question Video: Addition and Subtraction of Algebraic Expressions Mathematics • 7th Grade

Add 38π‘₯ βˆ’ 33𝑦 + 28𝑧, 24𝑦 βˆ’ 23π‘₯ βˆ’ 23𝑧, and 24π‘₯ βˆ’ 11𝑧 βˆ’ 17𝑦, then subtract the result from 26π‘₯ βˆ’ 17𝑦 + 19𝑧.

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Video Transcript

Add 38π‘₯ minus 33𝑦 plus 28𝑧, 24𝑦 minus 23π‘₯ minus 23𝑧, and 24π‘₯ minus 11𝑧 minus 17𝑦 then subtract the result from 26π‘₯ minus 17𝑦 plus 19𝑧.

Our first step is to add the three expressions. In order to do this, we’ll group or collect the like terms. We’ll group the π‘₯s, then we’ll group the 𝑦s, then we’ll group the 𝑧s.

Grouping the π‘₯ terms gives us 38π‘₯ minus 23π‘₯ plus 24π‘₯. This is equal to 39π‘₯. Next, we’ll group the 𝑦 terms: negative 33𝑦 plus 24𝑦 minus 17𝑦. This is equal to negative 26𝑦 as negative 33 plus 24 minus 17 is equal to negative 26. Finally, we need to group the 𝑧 terms: 28𝑧 minus 23𝑧 minus 11𝑧. This is equal to minus six 𝑧 as 28 minus 23 minus 11 is equal to negative six.

Adding the three expressions 38π‘₯ minus 33𝑦 plus 28𝑧, 24𝑦 minus 23π‘₯ minus 23𝑧, and 24π‘₯ minus 11𝑧 minus 17𝑦 gives us 39π‘₯ minus 26𝑦 minus six 𝑧. We were then asked to subtract the result from 26π‘₯ minus 17𝑦 plus 19𝑧. This can be written as 26π‘₯ minus 17𝑦 plus 19𝑧 minus 39π‘₯ minus 26𝑦 minus six 𝑧.

Once again, we need to group the like terms. 26π‘₯ minus 39π‘₯ is negative 13π‘₯ as 26 minus 39 is negative 13. Negative 17𝑦 minus negative 26𝑦 is plus nine 𝑦 as negative 17 minus negative 26 is the same as negative 17 plus 26, which gives us an answer of nine. Finally, 19𝑧 minus negative six 𝑧 is equal to 25𝑧 as 19 minus negative six is equal to 25.

This means that our final answer is negative 13π‘₯ plus nine 𝑦 plus 25𝑧.

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