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Answer :
Answer:
n=12
Step-by-step explanation:
13 less than 9 times a number: 13 less than 9n, 9n-13
11 more than 7 times a number: 11 more than 7n, 7n+11
9n-13=7n+11
2n=24
n=12
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Final answer:
The word problem was translated to the equation 9x - 13 = 7x + 11. By solving this equation, the value of the unknown number was found to be x = 12. This solution was verified by substituting x back into the equation.
Explanation:
The problem requires us to translate a word problem into an equation and then solve for the unknown number. The statement given is: "Thirteen less than nine times a number is equal to 11 more than seven times the number." To translate this into an algebraic equation, we define the unknown number as x. Then we express the sentence in symbols:
9x - 13 = 7x + 11
To solve for x, we first isolate the variable on one side by subtracting 7x from both sides of the equation:
2x - 13 = 11
Next, we add 13 to both sides to solve for 2x:
2x = 24
Finally, we divide both sides by 2 to find the value of x:
x = 12
Therefore, the solution is x = 12, which means the original number we were looking for is 12. To check the answer, we can substitute the value of x back into the original equation to see if both sides are equal:
9(12) - 13 = 7(12) + 11
108 - 13 = 84 + 11
95 = 95
Since both sides are equal, our solution x = 12 is correct.
