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Question1. Solve and check: 3t+7=−83t + 7 = -8
2. Solve and check: 8=16+8n8 = 16 + 8n
3. Solve and check: −34=6m−4-34 = 6m - 4
4. Solve and check: 9x+27=−729x + 27 = -72
5. Solve and check: y5−6=8\frac{y}{5} - 6 = 8

Studdy Solution

STEP 1

Assumptions1. We are given the equations - 3t+7=−83t +7 = -8 - 8=16+8n8 =16 +8n - −34=6m−4-34 =6m -4 - 9x+27=−729x +27 = -72 - y5−6=8\frac{y}{5} -6 =8 . We are to solve for the variables tt, nn, mm, xx, and yy respectively using properties of equality.

STEP 2

Let's solve the first equation t+7=−8t +7 = -8.
The first step is to isolate the term with the variable on one side of the equation. We can do this by subtracting7 from both sides of the equation.
t+7−7=−8−7t +7 -7 = -8 -7

STEP 3

implify the equation.
3t=−153t = -15

STEP 4

Next, we divide both sides of the equation by3 to solve for tt.
t=−153t = \frac{-15}{3}

STEP 5

Calculate the value of tt.
t=−5t = -5

STEP 6

Check the solution by substituting t=−5t = -5 back into the original equation.
3(−5)+=−83(-5) + = -8

STEP 7

implify the left side of the equation.
−15+7=−-15 +7 = -

STEP 8

implify further to confirm that both sides of the equation are equal.
−8=−8-8 = -8

STEP 9

Now, let's solve the second equation 8=16+8n8 =16 +8n.
First, subtract16 from both sides of the equation.
8−16=16+8n−168 -16 =16 +8n -16

STEP 10

implify the equation.
−8=8n-8 =8n

STEP 11

Next, divide both sides of the equation by8 to solve for nn.
n=−88n = \frac{-8}{8}

STEP 12

Calculate the value of nn.
n=−n = -

STEP 13

Check the solution by substituting n=−n = - back into the original equation.
8=16+8(−)8 =16 +8(-)

STEP 14

implify the right side of the equation.
8=16−88 =16 -8

STEP 15

implify further to confirm that both sides of the equation are equal.
8=88 =8

STEP 16

Now, let's solve the third equation −34=6m−4-34 =6m -4.
First, add4 to both sides of the equation.
−34+4=6m−4+4-34 +4 =6m -4 +4

STEP 17

implify the equation.
−30=6m-30 =6m

STEP 18

Next, divide both sides of the equation by6 to solve for mm.
m=−306m = \frac{-30}{6}

STEP 19

Calculate the value of mm.
m=−5m = -5

STEP 20

Check the solution by substituting m=−5m = -5 back into the original equation.
−34=6(−5)−4-34 =6(-5) -4

STEP 21

implify the right side of the equation.
−34=−30−4-34 = -30 -4

STEP 22

implify further to confirm that both sides of the equation are equal.
−34=−34-34 = -34

STEP 23

Now, let's solve the fourth equation 9x+27=−729x +27 = -72.
First, subtract27 from both sides of the equation.
9x+27−27=−72−279x +27 -27 = -72 -27

STEP 24

implify the equation.
9x=−999x = -99

STEP 25

Next, divide both sides of the equation by9 to solve for xx.
x=−999x = \frac{-99}{9}

STEP 26

Calculate the value of xx.
x=−11x = -11

STEP 27

Check the solution by substituting x=−11x = -11 back into the original equation.
9(−11)+27=−729(-11) +27 = -72

STEP 28

implify the left side of the equation.
−99+27=−72-99 +27 = -72

STEP 29

implify further to confirm that both sides of the equation are equal.
−72=−72-72 = -72

STEP 30

Finally, let's solve the fifth equation y5−6=8\frac{y}{5} -6 =8.
First, add6 to both sides of the equation.
y5−6+6=8+6\frac{y}{5} -6 +6 =8 +6

STEP 31

implify the equation.
y5=14\frac{y}{5} =14

STEP 32

Next, multiply both sides of the equation by5 to solve for yy.
y=14×5y =14 \times5

STEP 33

Calculate the value of yy.
y=70y =70

STEP 34

Check the solution by substituting y=70y =70 back into the original equation.
70−6=8\frac{70}{} -6 =8

STEP 35

implify the left side of the equation.
14−=814 - =8

STEP 36

implify further to confirm that both sides of the equation are equal.
8=88 =8The solutions to the equations are t=−5t = -5, n=−1n = -1, m=−5m = -5, x=−11x = -11, and y=70y =70.

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