Twice the difference of a number and 5 is 2. Use the variable W for the unknown number

1 answer:

8 0

Hey there!

The difference of a number, w, and 5 will be represented by (w – 5). Twice this would simply multiply this expression by 2, making it 2(w – 5). Finally, just set this expression equal to 2. Your equation is 2(w – 5) = 2.

To solve this, expand the two to the terms in parentheses. Then, solve the rest of the way as you would normally, using addition, subtraction, multiplication, or division to cancel out and move around terms. Remember, what you do on one side must be done to the other!

2(w – 5) = 2
(2*w – 2*5) = 2
(2w – 10) + 10 = (2) + 10
(2w) ÷ 2 = (12) ÷ 2
w = 6

Hope this helped you out! :-)

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<em>There are 142 whole numbers less than 1000 and divisible by 7.</em>

Step-by-step explanation:

The multiples of 7 form an arithmetic sequence like shown:

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The last term of this sequence can be found by dividing 1000/7=142.9 and rounding down to the previous integer: 142*7= 994.

Thus, the sequence has:

a1=7, r=7, an=994. We need to find n and we'll do that by using the general term formula:

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And solving for n:

$\displaystyle n= \frac{a_n-a_1}{r}+1$

$\displaystyle n= \frac{994-7}{7}+1$

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