Studdy AI Logo
Math

Question Solve for the variable in each equation. Write final solution as an equation.
1. −8t+4=−60-8t + 4 = -60
2. 3=6−3z3 = 6 - 3z
3. 65d+1=−11\frac{6}{5}d + 1 = -11
4. −16x−4=−1-\frac{1}{6}x - 4 = -1

Studdy Solution

STEP 1

Assumptions
1. We are solving for the variable in each given equation.
2. We will perform algebraic operations to isolate the variable on one side of the equation.
3. We will maintain the equality of each equation by performing the same operation on both sides.

STEP 2

Solve the first equation −8t+4=−60-8t + 4 = -60.

STEP 3

Subtract 4 from both sides to isolate the term containing tt.
−8t+4−4=−60−4-8t + 4 - 4 = -60 - 4

STEP 4

Simplify both sides of the equation.
−8t=−64-8t = -64

STEP 5

Divide both sides by −8-8 to solve for tt.
−8t−8=−64−8\frac{-8t}{-8} = \frac{-64}{-8}

STEP 6

Calculate the value of tt.
t=8t = 8

STEP 7

Write the final solution for the first equation.
t=8t = 8

STEP 8

Solve the second equation 3=6−3z3 = 6 - 3z.

STEP 9

Subtract 6 from both sides to isolate the term containing zz.
3−6=6−6−3z3 - 6 = 6 - 6 - 3z

STEP 10

Simplify both sides of the equation.
−3=−3z-3 = -3z

STEP 11

Divide both sides by −3-3 to solve for zz.
−3−3=−3z−3\frac{-3}{-3} = \frac{-3z}{-3}

STEP 12

Calculate the value of zz.
z=1z = 1

STEP 13

Write the final solution for the second equation.
z=1z = 1

STEP 14

Solve the third equation 65d+1=−11\frac{6}{5}d + 1 = -11.

STEP 15

Subtract 1 from both sides to isolate the term containing dd.
65d+1−1=−11−1\frac{6}{5}d + 1 - 1 = -11 - 1

STEP 16

Simplify both sides of the equation.
65d=−12\frac{6}{5}d = -12

STEP 17

Multiply both sides by 56\frac{5}{6} to solve for dd.
56⋅65d=−12⋅56\frac{5}{6} \cdot \frac{6}{5}d = -12 \cdot \frac{5}{6}

STEP 18

Calculate the value of dd.
d=−10d = -10

STEP 19

Write the final solution for the third equation.
d=−10d = -10

STEP 20

Solve the fourth equation −16x−4=−1-\frac{1}{6}x - 4 = -1.

STEP 21

Add 4 to both sides to isolate the term containing xx.
−16x−4+4=−1+4-\frac{1}{6}x - 4 + 4 = -1 + 4

STEP 22

Simplify both sides of the equation.
−16x=3-\frac{1}{6}x = 3

STEP 23

Multiply both sides by −6-6 to solve for xx.
−6⋅−16x=3⋅−6-6 \cdot -\frac{1}{6}x = 3 \cdot -6

STEP 24

Calculate the value of xx.
x=−18x = -18

STEP 25

Write the final solution for the fourth equation.
x=−18x = -18
The solutions for the given equations are: \begin{tabular}{|c|c|} \hline \hline Equation & Solution \\ \hline \hline−8t+4=−60-8 t+4=-60 & t=8t = 8 \\ \hline \hline 3=6−3z3=6-3 z & z=1z = 1 \\ \hline \hline65d+1=−11\frac{6}{5} d+1=-11 & d=−10d = -10 \\ \hline \hline−16x−4=−1-\frac{1}{6} x-4=-1 & x=−18x = -18 \\ \hline \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