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Solve the equations for the following problems.
For the following problems, translate the phrases or sentences to mathematical expressions or equations.
A quantity less eight.
Negative ten minus some number.
One seventh of a number plus two ninths of the number.
Twice a quantity plus nine is equal to the quantity plus sixty.
Four times a number minus five is divided by seven. The result is ten more than the number.
A number is added to itself five times, and that result is multiplied by eight. The entire result is twelve.
A quantity less three is divided by two more than the quantity itself. The result is one less than the original quantity.
A number is divided by twice the number, and eight times the number is added to that result. The result is negative one.
An unknown quantity is decreased by six. This result is then divided by twenty. Ten is subtracted from this result and negative two is obtained.
One less than some number is divided by five times the number. The result is the cube of the number.
Nine less than some number is multiplied by the number less nine. The result is the square of six times the number.
For the following problems, find the solution.
This year an item costs $106, an increase of $10 over last year’s price. What was last year’s price?
The perimeter of a square is 44 inches. Find the length of a side.
Two consecutive integers sum to 63. What are they?
If twenty-one is subtracted from some number and that result is multiplied by two, the result is thirty-eight. What is the number?
A statistician is collecting data to help her estimate the number of pickpockets in a certain city. She needs 108 pieces of data and is done. How many pieces of data has she collected?
The statistician in problem 78 is eight pieces of data short of being done. How many pieces of data has she collected?
A television commercial advertises that a certain type of light bulb will last, on the average, 200 hours longer than three times the life of another type of bulb. If consumer tests show that the advertised bulb lasts 4700 hours, how many hours must the other type of bulb last for the advertiser’s claim to be valid?
Solve the inequalities for the following problems.
What numbers satisfy the condition: nine less than negative four times a number is strictly greater than negative one?
Solve the equations for the following problems.
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