Math / Algebra

QuestionEvaluate the expression when $\begin{array}{c} \mathrm{Bx}=10 \text { and } y=-\frac{2}{y} \\ 3 x+2 y \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to plug in the values of $x$ and $y$ into the expression $3x + 2y$ and simplify it! Watch out! Be careful with the negative sign when substituting $y$ !
Double negatives can be tricky.

STEP 2

1. Substitute the values
2. Simplify the expression

STEP 3

Let's start by substituting the value of $x$ , which is $x = 10$ , into our expression $3x + 2y$ .
This gives us $3 \cdot (\mathbf{10}) + 2y$ .
Remember, we're multiplying 3 and 10!

STEP 4

Now, let's substitute the value of $y$ , which is $y = -\frac{2}{3}$ , into our expression $3 \cdot 10 + 2y$ .
This gives us $3 \cdot 10 + 2 \cdot \left( \mathbf{-\frac{2}{3}} \right)$ .
Don't forget those parentheses; they're important for keeping the negative sign with the fraction.

STEP 5

First, let's multiply the numbers: $3 \cdot 10$ gives us $\mathbf{30}$ , and $2 \cdot \left( -\frac{2}{3} \right)$ gives us $\mathbf{-\frac{4}{3}}$ .
So, our expression becomes $30 - \frac{4}{3}$ .
See how we handled that negative?

STEP 6

To subtract fractions, we need a common denominator.
Here, it's 3.
We can rewrite 30 as $\frac{30 \cdot 3}{3}$ , which is $\frac{\mathbf{90}}{3}$ .
Now our expression is $\frac{90}{3} - \frac{4}{3}$ .

STEP 7

Now that we have a common denominator, we can subtract the fractions: $\frac{90}{3} - \frac{4}{3} = \frac{\mathbf{86}}{3}$ .
Awesome!

STEP 8

Our final answer is $\frac{86}{3}$ !

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QuestionEvaluate the expression when $\begin{array}{c} \mathrm{Bx}=10 \text { and } y=-\frac{2}{y} \\ 3 x+2 y \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to plug in the values of $x$ and $y$ into the expression $3x + 2y$ and simplify it! Watch out! Be careful with the negative sign when substituting $y$ !
Double negatives can be tricky.

STEP 2

1. Substitute the values
2. Simplify the expression

STEP 3

Let's start by substituting the value of $x$ , which is $x = 10$ , into our expression $3x + 2y$ .
This gives us $3 \cdot (\mathbf{10}) + 2y$ .
Remember, we're multiplying 3 and 10!

STEP 4

Now, let's substitute the value of $y$ , which is $y = -\frac{2}{3}$ , into our expression $3 \cdot 10 + 2y$ .
This gives us $3 \cdot 10 + 2 \cdot \left( \mathbf{-\frac{2}{3}} \right)$ .
Don't forget those parentheses; they're important for keeping the negative sign with the fraction.

STEP 5

First, let's multiply the numbers: $3 \cdot 10$ gives us $\mathbf{30}$ , and $2 \cdot \left( -\frac{2}{3} \right)$ gives us $\mathbf{-\frac{4}{3}}$ .
So, our expression becomes $30 - \frac{4}{3}$ .
See how we handled that negative?

STEP 6

To subtract fractions, we need a common denominator.
Here, it's 3.
We can rewrite 30 as $\frac{30 \cdot 3}{3}$ , which is $\frac{\mathbf{90}}{3}$ .
Now our expression is $\frac{90}{3} - \frac{4}{3}$ .

STEP 7

Now that we have a common denominator, we can subtract the fractions: $\frac{90}{3} - \frac{4}{3} = \frac{\mathbf{86}}{3}$ .
Awesome!

STEP 8

Our final answer is $\frac{86}{3}$ !

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QuestionEvaluate the expression when Bx=10 and y=−2y3x+2y\begin{array}{c} \mathrm{Bx}=10 \text { and } y=-\frac{2}{y} \\ 3 x+2 y \end{array}Bx=10 and y=−y2​3x+2y​

Studdy Solution

STEP 1

What is this asking? We need to plug in the values of xxx and yyy into the expression 3x+2y3x + 2y3x+2y and simplify it! Watch out! Be careful with the negative sign when substituting yyy!Double negatives can be tricky.

STEP 2

1. Substitute the values2. Simplify the expression

STEP 3

Let's **start** by substituting the value of xxx, which is x=10x = 10x=10, into our expression 3x+2y3x + 2y3x+2y.This gives us 3⋅(10)+2y3 \cdot (\mathbf{10}) + 2y3⋅(10)+2y.Remember, we're multiplying 3 and 10!

STEP 4

STEP 5

First, let's multiply the numbers: 3⋅103 \cdot 103⋅10 gives us 30\mathbf{30}30, and 2⋅(−23)2 \cdot \left( -\frac{2}{3} \right)2⋅(−32​) gives us −43\mathbf{-\frac{4}{3}}−34​.So, our expression becomes 30−4330 - \frac{4}{3}30−34​.See how we handled that negative?

STEP 6

To subtract fractions, we need a common denominator.Here, it's 3.We can rewrite 30 as 30⋅33\frac{30 \cdot 3}{3}330⋅3​, which is 903\frac{\mathbf{90}}{3}390​.Now our expression is 903−43\frac{90}{3} - \frac{4}{3}390​−34​.

STEP 7

Now that we have a common denominator, we can subtract the fractions: 903−43=863\frac{90}{3} - \frac{4}{3} = \frac{\mathbf{86}}{3}390​−34​=386​.Awesome!

STEP 8

Our **final answer** is 863\frac{86}{3}386​!

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionEvaluate the expression when $\begin{array}{c} \mathrm{Bx}=10 \text { and } y=-\frac{2}{y} \\ 3 x+2 y \end{array}$

What is this asking? We need to plug in the values of $x$ and $y$ into the expression $3x + 2y$ and simplify it! Watch out! Be careful with the negative sign when substituting $y$ !
Double negatives can be tricky.

1. Substitute the values
2. Simplify the expression

Let's start by substituting the value of $x$ , which is $x = 10$ , into our expression $3x + 2y$ .
This gives us $3 \cdot (\mathbf{10}) + 2y$ .
Remember, we're multiplying 3 and 10!

First, let's multiply the numbers: $3 \cdot 10$ gives us $\mathbf{30}$ , and $2 \cdot \left( -\frac{2}{3} \right)$ gives us $\mathbf{-\frac{4}{3}}$ .
So, our expression becomes $30 - \frac{4}{3}$ .
See how we handled that negative?

To subtract fractions, we need a common denominator.
Here, it's 3.
We can rewrite 30 as $\frac{30 \cdot 3}{3}$ , which is $\frac{\mathbf{90}}{3}$ .
Now our expression is $\frac{90}{3} - \frac{4}{3}$ .

Now that we have a common denominator, we can subtract the fractions: $\frac{90}{3} - \frac{4}{3} = \frac{\mathbf{86}}{3}$ .
Awesome!

Our final answer is $\frac{86}{3}$ !