Math / Algebra

QuestionWhich equations have the same value of $x$ as $\frac{5}{6} x+\frac{2}{3}=-9$ ? Select three options. $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9$ $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ $5 x+4=-54$ $5 x+4=-9$ $5 x=-13$ $5 x=-58$

Studdy Solution

STEP 1

What is this asking? We need to find three equations that have the same solution for $x$ as the given equation $\frac{5}{6} x+\frac{2}{3}=-9$ . Watch out! Don't forget to multiply both sides of the equation when trying to get rid of fractions.
It's easy to miss a term!

STEP 2

1. Solve the original equation
2. Check the options

STEP 3

Let's multiply both sides of the equation $\frac{5}{6} x+\frac{2}{3}=-9$ by 6 to get rid of those pesky fractions!
We do this because $\frac{5}{6} \cdot 6 = 5$ and $\frac{2}{3} \cdot 6 = \frac{12}{3} = 4$ .
We're basically dividing to one!
This gives us: $6 \cdot \left(\frac{5}{6} x+\frac{2}{3}\right) = 6 \cdot (-9)$

STEP 4

Now we simplify! $5x + 4 = -54$ Look at that, no more fractions!

STEP 5

To isolate the term with $x$ , we'll subtract 4 from both sides of the equation: $5x + 4 - 4 = -54 - 4$ $5x = -58$

STEP 6

Almost there!
Now we divide both sides by 5 to solve for $x$ : $\frac{5x}{5} = \frac{-58}{5}$ $x = -\frac{58}{5}$ So, our final solution for the original equation is $x = -\frac{58}{5}$ .

STEP 7

Now, let's look at the options and see which ones match our solution or steps along the way.
We found $x = -\frac{58}{5}$ , and the intermediate steps were $5x + 4 = -54$ and $5x = -58$ .

STEP 8

We can see that $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ is the same as our first step after multiplying both sides by 6. $5 x+4=-54$ is the simplified version from our second step.
And $5x = -58$ is the result from our third step.

STEP 9

The three equations that have the same solution are: $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ $5 x+4=-54$ $5 x=-58$

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QuestionWhich equations have the same value of $x$ as $\frac{5}{6} x+\frac{2}{3}=-9$ ? Select three options. $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9$ $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ $5 x+4=-54$ $5 x+4=-9$ $5 x=-13$ $5 x=-58$

Studdy Solution

STEP 1

What is this asking? We need to find three equations that have the same solution for $x$ as the given equation $\frac{5}{6} x+\frac{2}{3}=-9$ . Watch out! Don't forget to multiply both sides of the equation when trying to get rid of fractions.
It's easy to miss a term!

STEP 2

1. Solve the original equation
2. Check the options

STEP 3

STEP 4

Now we simplify! $5x + 4 = -54$ Look at that, no more fractions!

STEP 5

To isolate the term with $x$ , we'll subtract 4 from both sides of the equation: $5x + 4 - 4 = -54 - 4$ $5x = -58$

STEP 6

Almost there!
Now we divide both sides by 5 to solve for $x$ : $\frac{5x}{5} = \frac{-58}{5}$ $x = -\frac{58}{5}$ So, our final solution for the original equation is $x = -\frac{58}{5}$ .

STEP 7

Now, let's look at the options and see which ones match our solution or steps along the way.
We found $x = -\frac{58}{5}$ , and the intermediate steps were $5x + 4 = -54$ and $5x = -58$ .

STEP 8

We can see that $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ is the same as our first step after multiplying both sides by 6. $5 x+4=-54$ is the simplified version from our second step.
And $5x = -58$ is the result from our third step.

STEP 9

The three equations that have the same solution are: $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ $5 x+4=-54$ $5 x=-58$

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Studdy Solution

STEP 1

What is this asking? We need to find three equations that have the same solution for xxx as the given equation 56x+23=−9\frac{5}{6} x+\frac{2}{3}=-965​x+32​=−9. Watch out! Don't forget to multiply *both* sides of the equation when trying to get rid of fractions.It's easy to miss a term!

STEP 2

1. Solve the original equation2. Check the options

STEP 3

STEP 4

Now we **simplify**! 5x+4=−545x + 4 = -545x+4=−54 Look at that, no more fractions!

STEP 5

To **isolate** the term with xxx, we'll **subtract 4** from both sides of the equation: 5x+4−4=−54−45x + 4 - 4 = -54 - 45x+4−4=−54−4 5x=−585x = -585x=−58

STEP 6

Almost there!Now we **divide both sides** by **5** to solve for xxx: 5x5=−585\frac{5x}{5} = \frac{-58}{5}55x​=5−58​ x=−585x = -\frac{58}{5}x=−558​So, our **final solution** for the original equation is x=−585x = -\frac{58}{5}x=−558​.

STEP 7

Now, let's look at the options and see which ones match our solution or steps along the way.We found x=−585x = -\frac{58}{5}x=−558​, and the intermediate steps were 5x+4=−545x + 4 = -545x+4=−54 and 5x=−585x = -585x=−58.

STEP 8

STEP 9

The three equations that have the same solution are: 6(56x+23)=−9(6)6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)6(65​x+32​)=−9(6) 5x+4=−545 x+4=-545x+4=−545x=−585 x=-585x=−58

Get Studdy

Studdy solves anything!

Start learning now

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

What is this asking? We need to find three equations that have the same solution for $x$ as the given equation $\frac{5}{6} x+\frac{2}{3}=-9$ . Watch out! Don't forget to multiply both sides of the equation when trying to get rid of fractions.
It's easy to miss a term!

1. Solve the original equation
2. Check the options

Now we simplify! $5x + 4 = -54$ Look at that, no more fractions!

To isolate the term with $x$ , we'll subtract 4 from both sides of the equation: $5x + 4 - 4 = -54 - 4$ $5x = -58$

Almost there!
Now we divide both sides by 5 to solve for $x$ : $\frac{5x}{5} = \frac{-58}{5}$ $x = -\frac{58}{5}$ So, our final solution for the original equation is $x = -\frac{58}{5}$ .

Now, let's look at the options and see which ones match our solution or steps along the way.
We found $x = -\frac{58}{5}$ , and the intermediate steps were $5x + 4 = -54$ and $5x = -58$ .

The three equations that have the same solution are: $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$ $5 x+4=-54$ $5 x=-58$