Math / Algebra

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The table shows the scores of two teams at the end of the first half of a trivia challenge. \begin{tabular}{|c|c|} \hline Team & Points Scored \\ \hline Bobcats & $2 x-7$ \\ \hline Huskies & $5 x-3$ \\ \hline \end{tabular}
How many more points did the Huskies score than the Bobcats? $\qquad$ point(s) $\qquad$ () Need help with this question?

Studdy Solution

STEP 1

What is this asking? We need to find the difference in points between the Huskies and the Bobcats. Watch out! Make sure to subtract the Bobcats' score from the Huskies' score, not the other way around!

STEP 2

1. Set up the subtraction
2. Simplify the expression

STEP 3

Alright, so the Huskies scored $5x - 3$ points, and the Bobcats scored $2x - 7$ points.
We want to find how many more points the Huskies scored, so we'll subtract the Bobcats' score from the Huskies' score.
This gives us: $(5x - 3) - (2x - 7)$

STEP 4

Remember that subtracting is the same as adding the opposite.
So, we can distribute the negative sign to the terms inside the parentheses: $5x - 3 + (-1) \cdot 2x + (-1) \cdot (-7)$ $5x - 3 - 2x + 7$

STEP 5

Now, let's combine the $x$ terms and the constant terms: $(5x - 2x) + (-3 + 7)$ $3x + 4$

STEP 6

The Huskies scored $3x + 4$ more points than the Bobcats.

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Studdy Solution

STEP 1

What is this asking? We need to find the difference in points between the Huskies and the Bobcats. Watch out! Make sure to subtract the Bobcats' score from the Huskies' score, not the other way around!

STEP 2

1. Set up the subtraction
2. Simplify the expression

STEP 3

Alright, so the Huskies scored $5x - 3$ points, and the Bobcats scored $2x - 7$ points.
We want to find how many more points the Huskies scored, so we'll subtract the Bobcats' score from the Huskies' score.
This gives us: $(5x - 3) - (2x - 7)$

STEP 4

Remember that subtracting is the same as adding the opposite.
So, we can distribute the negative sign to the terms inside the parentheses: $5x - 3 + (-1) \cdot 2x + (-1) \cdot (-7)$ $5x - 3 - 2x + 7$

STEP 5

Now, let's combine the $x$ terms and the constant terms: $(5x - 2x) + (-3 + 7)$ $3x + 4$

STEP 6

The Huskies scored $3x + 4$ more points than the Bobcats.

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Studdy Solution

STEP 1

What is this asking? We need to find the difference in points between the Huskies and the Bobcats. Watch out! Make sure to subtract the Bobcats' score from the Huskies' score, not the other way around!

STEP 2

1. Set up the subtraction2. Simplify the expression

STEP 3

Alright, so the Huskies scored 5x−35x - 35x−3 points, and the Bobcats scored 2x−72x - 72x−7 points.We want to find how many *more* points the Huskies scored, so we'll subtract the Bobcats' score from the Huskies' score.This gives us: (5x−3)−(2x−7)(5x - 3) - (2x - 7)(5x−3)−(2x−7)

STEP 4

Remember that subtracting is the same as adding the opposite.So, we can distribute the negative sign to the terms inside the parentheses: 5x−3+(−1)⋅2x+(−1)⋅(−7)5x - 3 + (-1) \cdot 2x + (-1) \cdot (-7)5x−3+(−1)⋅2x+(−1)⋅(−7) 5x−3−2x+75x - 3 - 2x + 75x−3−2x+7

STEP 5

Now, let's combine the **xxx terms** and the **constant terms**: (5x−2x)+(−3+7)(5x - 2x) + (-3 + 7)(5x−2x)+(−3+7) 3x+43x + 43x+4

STEP 6

The Huskies scored 3x+43x + 43x+4 more points than the Bobcats.

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1. Set up the subtraction
2. Simplify the expression

Alright, so the Huskies scored $5x - 3$ points, and the Bobcats scored $2x - 7$ points.
We want to find how many more points the Huskies scored, so we'll subtract the Bobcats' score from the Huskies' score.
This gives us: $(5x - 3) - (2x - 7)$

Remember that subtracting is the same as adding the opposite.
So, we can distribute the negative sign to the terms inside the parentheses: $5x - 3 + (-1) \cdot 2x + (-1) \cdot (-7)$ $5x - 3 - 2x + 7$

Now, let's combine the $x$ terms and the constant terms: $(5x - 2x) + (-3 + 7)$ $3x + 4$

The Huskies scored $3x + 4$ more points than the Bobcats.