Math

Question Find the value of 2k2k when kk more than 7 subtracted from 18 results in 2.

Studdy Solution

STEP 1

Assumptions
1. The expression for subtracting k\mathrm{k} more than 7 from 18 is 18(k+7)18 - (\mathrm{k} + 7).
2. The result of this subtraction is 2.
3. We need to solve for k\mathrm{k}.
4. After finding the value of k\mathrm{k}, we need to calculate 2k2\mathrm{k}.

STEP 2

Set up the equation based on the given information.
18(k+7)=218 - (\mathrm{k} + 7) = 2

STEP 3

Simplify the equation by distributing the negative sign inside the parentheses.
18k7=218 - \mathrm{k} - 7 = 2

STEP 4

Combine like terms on the left side of the equation.
11k=211 - \mathrm{k} = 2

STEP 5

Isolate k\mathrm{k} by adding k\mathrm{k} to both sides of the equation.
11=2+k11 = 2 + \mathrm{k}

STEP 6

Subtract 2 from both sides to solve for k\mathrm{k}.
112=k11 - 2 = \mathrm{k}

STEP 7

Calculate the value of k\mathrm{k}.
k=112=9\mathrm{k} = 11 - 2 = 9

STEP 8

Now that we have the value of k\mathrm{k}, we can find the value of 2k2\mathrm{k}.
2k=2×92\mathrm{k} = 2 \times 9

STEP 9

Calculate the value of 2k2\mathrm{k}.
2k=2×9=182\mathrm{k} = 2 \times 9 = 18
The value of 2k2\mathrm{k} is 18, which corresponds to option (E).

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