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solve linear equations for word problems

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Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check
Solve the inequality and graph the solution set on a number line:
6) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:
4(z+3)/3 = 10 -2z

7) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:
0.03(k + 7) - 0.02(5- k) = 0.01

8) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:
5/6x + 2 = 1/3x

9) Solve the inequality and graph the solution set on a number line:
5x - 7 >= 8x + 5

10) Solve the inequality and graph the solution set on a number line:
-5 < 4 - 3x <= 7

III. Word problems (5 points each). Please show all work and include appropriate units in your answers.

1) According to the National Weather Service, the record high temperature on June 26th in Washington, DC was 38&#730; C in 1952, and the record low temperature on June 26th in Washington, DC was 13 C in 1979. If the formula for converting temperatures from degrees Celsius to degrees Fahrenheit is F=9/5C + 32 , what were the record high and low temperatures for this date in degrees Fahrenheit? You may round to the nearest whole number.

2) Leah is buying a new home. She finds a house that she likes that is priced at $287,500. If she is told that the house has increased in price by 25% since it last sold, what was the price the last time it sold?

3) Tamara wins $20,000 (after taxes) in a sweepstakes and decides to deposit all of it in two accounts. One account is a college savings account that guarantees a rate of 5.5% simple annual interest. The other account is a money market fund that does not do as well as Tamara had hoped, and only returns a simple annual interest rate of 4.8%. If the two accounts together earn $1072 by the end of the year, how much money did she deposit in each account?

4) Gail is helping her daughter's school PTA plan a graduation party for the seniors. The PTA has budgeted $6000 for the party at a local hotel, which charges a $750 rental fee plus $35/person. Find the greatest number of students that can attend the party without the PTA exceeding its budget. (Chaperones attend the party at no cost).

5) Jenn and Adele decide to perform an algebra experiment. They set out from their respective homes (in Anchorage and Boulder) and drive steadily toward each other on an agreed-upon route. If the total distance along this route between their homes is 3000 miles, and if Jenn averages 65 mph and Adele averages 55 mph, how long will it take them to meet?

6) Simplify the expression and write the result in lowest terms:

7) Simplify the expression and write the result in lowest terms

3) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:
3(w -2) - (12 - w) =2

4) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:
x/(-4) = -2

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Solution Summary

It provides detailed explainations to a set of algebra questions, including linear equations, word problems, and simplifying rational expressions.

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6) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:

Multiply 3 to each side of the equation:

Remove the parenthesis:

Move z terms to left side, and other terms to the right side:

Combine the link terms:

Check:
Left side:
Right side:
Left = right

7) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:

Remove the parentheses:

Combine the link terms:

Move other terms to the right side:

Check:
Left: = right

8) Solve the equation and check your answer, if possible, in the original equation. Show all work, including the check:

The LCD (least common denominator) is 6. so multiply 6 to both sides of the equation

Move x terms to the left side, and other terms to the right, then combine the like terms:

Check:
Left:
Right:
Left = right

9) Solve the inequality and graph the solution set on a number line:
Move x terms to the left and other terms to the right:

Divide -3 from both sides of the equation (remember to change the sign of the inequality when dividing a negative number):

10) Solve the ...

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