Solved on Jan 09, 2024

Find which values of the variable satisfy the given equations: $d+9=35$ with $d=16,22,26,36$ , and $14 n=35$ with $n=2,3,3.5,4$ .

STEP 1

Assumptions
1. We are given an equation $d+9=35$ and a set of values for $d$ which are $16, 22, 26, 36$ .
2. We are also given an equation $14n=35$ and a set of values for $n$ which are $2, 3, 3.5, 4$ .
3. We need to substitute each value into the respective equation to determine if it satisfies the equation.

STEP 2

Start with the first equation $d+9=35$ and substitute the first value of $d=16$ .
$d+9=35$ $16+9=35$

STEP 3

Calculate the sum to check if the equation holds true for $d=16$ .
$16+9=25$

STEP 4

Since $25 \neq 35$ , the value $d=16$ is not a solution to the equation $d+9=35$ .

STEP 5

Substitute the second value of $d=22$ into the equation.
$d+9=35$ $22+9=35$

STEP 6

Calculate the sum to check if the equation holds true for $d=22$ .
$22+9=31$

STEP 7

Since $31 \neq 35$ , the value $d=22$ is not a solution to the equation $d+9=35$ .

STEP 8

Substitute the third value of $d=26$ into the equation.
$d+9=35$ $26+9=35$

STEP 9

Calculate the sum to check if the equation holds true for $d=26$ .
$26+9=35$

STEP 10

Since $35 = 35$ , the value $d=26$ is a solution to the equation $d+9=35$ .

STEP 11

Substitute the fourth value of $d=36$ into the equation.
$d+9=35$ $36+9=35$

STEP 12

Calculate the sum to check if the equation holds true for $d=36$ .
$36+9=45$

STEP 13

Since $45 \neq 35$ , the value $d=36$ is not a solution to the equation $d+9=35$ .

STEP 14

Now, move on to the second equation $14n=35$ and substitute the first value of $n=2$ .
$14n=35$ $14 \cdot 2=35$

STEP 15

Calculate the product to check if the equation holds true for $n=2$ .
$14 \cdot 2=28$

STEP 16

Since $28 \neq 35$ , the value $n=2$ is not a solution to the equation $14n=35$ .

STEP 17

Substitute the second value of $n=3$ into the equation.
$14n=35$ $14 \cdot 3=35$

STEP 18

Calculate the product to check if the equation holds true for $n=3$ .
$14 \cdot 3=42$

STEP 19

Since $42 \neq 35$ , the value $n=3$ is not a solution to the equation $14n=35$ .

STEP 20

Substitute the third value of $n=3.5$ into the equation.
$14n=35$ $14 \cdot 3.5=35$

STEP 21

Calculate the product to check if the equation holds true for $n=3.5$ .
$14 \cdot 3.5=49$

STEP 22

Since $49 \neq 35$ , the value $n=3.5$ is not a solution to the equation $14n=35$ .

STEP 23

Substitute the fourth value of $n=4$ into the equation.
$14n=35$ $14 \cdot 4=35$

STEP 24

Calculate the product to check if the equation holds true for $n=4$ .
$14 \cdot 4=56$

STEP 25

Since $56 \neq 35$ , the value $n=4$ is not a solution to the equation $14n=35$ .

STEP 26

Summarize the solutions for both equations:
For the equation $d+9=35$ , the only solution is $d=26$ . For the equation $14n=35$ , there are no solutions from the given set of values.

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Find which values of the variable satisfy the given equations: d+9=35d+9=35d+9=35 with d=16,22,26,36d=16,22,26,36d=16,22,26,36, and 14n=3514 n=3514n=35 with n=2,3,3.5,4n=2,3,3.5,4n=2,3,3.5,4.

STEP 1

STEP 2

Start with the first equation d+9=35d+9=35d+9=35 and substitute the first value of d=16d=16d=16.d+9=35d+9=35d+9=35 16+9=3516+9=3516+9=35

STEP 3

Calculate the sum to check if the equation holds true for d=16d=16d=16.16+9=2516+9=2516+9=25

STEP 4

Since 25≠3525 \neq 3525=35, the value d=16d=16d=16 is not a solution to the equation d+9=35d+9=35d+9=35.

STEP 5

Substitute the second value of d=22d=22d=22 into the equation.d+9=35d+9=35d+9=35 22+9=3522+9=3522+9=35

STEP 6

Calculate the sum to check if the equation holds true for d=22d=22d=22.22+9=3122+9=3122+9=31

STEP 7

Since 31≠3531 \neq 3531=35, the value d=22d=22d=22 is not a solution to the equation d+9=35d+9=35d+9=35.

STEP 8

Substitute the third value of d=26d=26d=26 into the equation.d+9=35d+9=35d+9=35 26+9=3526+9=3526+9=35

STEP 9

Calculate the sum to check if the equation holds true for d=26d=26d=26.26+9=3526+9=3526+9=35

STEP 10

Since 35=3535 = 3535=35, the value d=26d=26d=26 is a solution to the equation d+9=35d+9=35d+9=35.

STEP 11

Substitute the fourth value of d=36d=36d=36 into the equation.d+9=35d+9=35d+9=35 36+9=3536+9=3536+9=35

STEP 12

Calculate the sum to check if the equation holds true for d=36d=36d=36.36+9=4536+9=4536+9=45

STEP 13

Since 45≠3545 \neq 3545=35, the value d=36d=36d=36 is not a solution to the equation d+9=35d+9=35d+9=35.

STEP 14

Now, move on to the second equation 14n=3514n=3514n=35 and substitute the first value of n=2n=2n=2.14n=3514n=3514n=35 14⋅2=3514 \cdot 2=3514⋅2=35

STEP 15

Calculate the product to check if the equation holds true for n=2n=2n=2.14⋅2=2814 \cdot 2=2814⋅2=28

STEP 16

Since 28≠3528 \neq 3528=35, the value n=2n=2n=2 is not a solution to the equation 14n=3514n=3514n=35.

STEP 17

Substitute the second value of n=3n=3n=3 into the equation.14n=3514n=3514n=35 14⋅3=3514 \cdot 3=3514⋅3=35

STEP 18

Calculate the product to check if the equation holds true for n=3n=3n=3.14⋅3=4214 \cdot 3=4214⋅3=42

STEP 19

Since 42≠3542 \neq 3542=35, the value n=3n=3n=3 is not a solution to the equation 14n=3514n=3514n=35.

STEP 20

Substitute the third value of n=3.5n=3.5n=3.5 into the equation.14n=3514n=3514n=35 14⋅3.5=3514 \cdot 3.5=3514⋅3.5=35

STEP 21

Calculate the product to check if the equation holds true for n=3.5n=3.5n=3.5.14⋅3.5=4914 \cdot 3.5=4914⋅3.5=49

STEP 22

Since 49≠3549 \neq 3549=35, the value n=3.5n=3.5n=3.5 is not a solution to the equation 14n=3514n=3514n=35.

STEP 23

Substitute the fourth value of n=4n=4n=4 into the equation.14n=3514n=3514n=35 14⋅4=3514 \cdot 4=3514⋅4=35

STEP 24

Calculate the product to check if the equation holds true for n=4n=4n=4.14⋅4=5614 \cdot 4=5614⋅4=56

STEP 25

Since 56≠3556 \neq 3556=35, the value n=4n=4n=4 is not a solution to the equation 14n=3514n=3514n=35.

STEP 26

Summarize the solutions for both equations:For the equation d+9=35d+9=35d+9=35, the only solution is d=26d=26d=26. For the equation 14n=3514n=3514n=35, there are no solutions from the given set of values.

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Find which values of the variable satisfy the given equations: $d+9=35$ with $d=16,22,26,36$ , and $14 n=35$ with $n=2,3,3.5,4$ .

Start with the first equation $d+9=35$ and substitute the first value of $d=16$ .
$d+9=35$ $16+9=35$

Calculate the sum to check if the equation holds true for $d=16$ .
$16+9=25$

Since $25 \neq 35$ , the value $d=16$ is not a solution to the equation $d+9=35$ .

Substitute the second value of $d=22$ into the equation.
$d+9=35$ $22+9=35$

Calculate the sum to check if the equation holds true for $d=22$ .
$22+9=31$

Since $31 \neq 35$ , the value $d=22$ is not a solution to the equation $d+9=35$ .

Substitute the third value of $d=26$ into the equation.
$d+9=35$ $26+9=35$

Calculate the sum to check if the equation holds true for $d=26$ .
$26+9=35$

Since $35 = 35$ , the value $d=26$ is a solution to the equation $d+9=35$ .

Substitute the fourth value of $d=36$ into the equation.
$d+9=35$ $36+9=35$

Calculate the sum to check if the equation holds true for $d=36$ .
$36+9=45$

Since $45 \neq 35$ , the value $d=36$ is not a solution to the equation $d+9=35$ .

Now, move on to the second equation $14n=35$ and substitute the first value of $n=2$ .
$14n=35$ $14 \cdot 2=35$

Calculate the product to check if the equation holds true for $n=2$ .
$14 \cdot 2=28$

Since $28 \neq 35$ , the value $n=2$ is not a solution to the equation $14n=35$ .

Substitute the second value of $n=3$ into the equation.
$14n=35$ $14 \cdot 3=35$

Calculate the product to check if the equation holds true for $n=3$ .
$14 \cdot 3=42$

Since $42 \neq 35$ , the value $n=3$ is not a solution to the equation $14n=35$ .

Substitute the third value of $n=3.5$ into the equation.
$14n=35$ $14 \cdot 3.5=35$

Calculate the product to check if the equation holds true for $n=3.5$ .
$14 \cdot 3.5=49$

Since $49 \neq 35$ , the value $n=3.5$ is not a solution to the equation $14n=35$ .

Substitute the fourth value of $n=4$ into the equation.
$14n=35$ $14 \cdot 4=35$

Calculate the product to check if the equation holds true for $n=4$ .
$14 \cdot 4=56$

Since $56 \neq 35$ , the value $n=4$ is not a solution to the equation $14n=35$ .

Summarize the solutions for both equations:
For the equation $d+9=35$ , the only solution is $d=26$ . For the equation $14n=35$ , there are no solutions from the given set of values.