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3 years ago

7(w+1)=5(2w-3)+1 Need Steps!

Mathematics

1 answer:

polet [3.4K]3 years ago

7 0

Answer:

w = 7

Step-by-step explanation:

7(w + 1) = 5 (2w - 3) + 1

Use distributive property

7w + 7 = 10w - 15 + 1

Add/subtract any same variables and numbers

7w + 7 = 10w - 14

Goal: isolate the variable (w)

Add 14 to both sides - this cancels out the 14 on the right side and transfers it to the left side

7w + 7 + 14 = 10w - 14 + 14

7w + 21 = 10w

Subtract 7w from both sides - this cancels out the 7w on the left side and transfers it to the right side

7w - 7w + 21 = 10w - 7w

21 = 10w - 7w

21 = 3w

Divide both sides by 3 - this cancels out the 3 on the right side and transfers it to the left side

21 ÷ 3 = 3w ÷ 3

3 divided by 3 = 1 (you do not have to add a 1 before a variable so the result is as follows)

21 ÷ 3 = w

Variable is now successfully isolated

7 = w

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D varies as R and S, and inversely as t. D=12, R=3, S=20, and t=5, find D when R=15, S=4 and t=8.

zavuch27 [327]

Given:

D varies as R and S, and inversely as t.

D=12, R=3, S=20, and t=5

To find:

The value of D when R=15, S=4 and t=8.

Solution:

It is given that D varies as R and S, and inversely as t. So,

$D\propto \dfrac{RS}{t}$

$D=\dfrac{kRS}{t}$ ...(i)

Where, k is the constant of proportionality.

We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get

$12=\dfrac{k(3)(20)}{5}$

$12=12k$

$\dfrac{12}{12}=k$

$1=k$

Substituting $k=1$ in (i), we get the required equation.

$D=\dfrac{(1)RS}{t}$

$D=\dfrac{RS}{t}$

We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get

$D=\dfrac{(15)(4)}{8}$

$D=\dfrac{60}{8}$

$D=7.5$

Therefore, the required value of D is 7.5.

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