Studdy AI Logo
Math

QuestionSolve these equations for xx: −35+x=125-\frac{3}{5}+x=\frac{12}{5}, x−5=−2x-5=-2, −6+x=−9-6+x=-9, x4=68\frac{x}{4}=\frac{6}{8}, −14x=−42-14x=-42, x3=9\frac{x}{3}=9. Place in table under x=3x=3 or x≠3x \neq 3.

Studdy Solution

STEP 1

Assumptions1. We are given a set of equations to solve for the variable x. . We need to categorize these equations under two categories x=3x=3 and x≠3x \neq3.
3. The solutions to the equations will determine their categories.

STEP 2

Let's start by solving the first equation −5+x=125-\frac{}{5}+x=\frac{12}{5} for x.

STEP 3

Add 35\frac{3}{5} to both sides of the equation to isolate x.
x=125+35x = \frac{12}{5} + \frac{3}{5}

STEP 4

Calculate the value of x.
x=15=3x = \frac{15}{} =3

STEP 5

The solution to the first equation is x=3x=3, so it belongs in the x=3x=3 category.

STEP 6

Next, solve the second equation x−5=−2x-5=-2 for x.

STEP 7

Add5 to both sides of the equation to isolate x.
x=−2+5x = -2 +5

STEP 8

Calculate the value of x.
x=3x =3

STEP 9

The solution to the second equation is x=3x=3, so it also belongs in the x=3x=3 category.

STEP 10

Now, solve the third equation −6+x=−9-6+x=-9 for x.

STEP 11

Add6 to both sides of the equation to isolate x.
x=−9+6x = -9 +6

STEP 12

Calculate the value of x.
x=−x = -

STEP 13

The solution to the third equation is x=−3x=-3, so it belongs in the x≠3x \neq3 category.

STEP 14

Next, solve the fourth equation x4=68\frac{x}{4}=\frac{6}{8} for x.

STEP 15

Multiply both sides of the equation by4 to isolate x.
x=4×8x =4 \times \frac{}{8}

STEP 16

Calculate the value of x.
x=3x =3

STEP 17

The solution to the fourth equation is x=3x=3, so it belongs in the x=3x=3 category.

STEP 18

Now, solve the fifth equation −14x=−42-14x=-42 for x.

STEP 19

Divide both sides of the equation by -14 to isolate x.
x=−42−14x = \frac{-42}{-14}

STEP 20

Calculate the value of x.
x=3x =3

STEP 21

The solution to the fifth equation is x=3x=3, so it also belongs in the x=3x=3 category.

STEP 22

Finally, solve the last equation x=9\frac{x}{}=9 for x.

STEP 23

Multiply both sides of the equation by3 to isolate x.
x=3×9x =3 \times9

STEP 24

Calculate the value of x.
x=27x =27

STEP 25

The solution to the last equation is x=27x=27, so it belongs in the x≠3x \neq3 category.

STEP 26

Now, we can place the equations in the correct categories.
\begin{tabular}{|l|l|} \hlinex=3x=3 & x≠3x \neq3 \\ \hline −35+x=125-\frac{3}{5}+x=\frac{12}{5} & −6+x=−9-6+x=-9 \\ \hline x−5=−x-5=- & x3=9\frac{x}{3}=9 \\ \hline x4=68\frac{x}{4}=\frac{6}{8} & \\ \hline −14x=−42-14x=-42 & \\ \end{tabular}

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord