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Algebra Calculations

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Can you please explain how to do these problems?
1. Evaluate 3x-4y/ 2z when x= -2, y=3, z=4 . Express your answer as a fraction.

2. Use the order of operations to simplify the following expression. (-2)2 -3 2

3. Write the statement as an algebraic equation: 'The difference between x and 2 is 4 more than twice x'

4. Name the property used in the equation: -2 (x+5) =-2x-10

5. Solve the following equation for x. 4(2x-3) +1= 6- 2 (x=4)

6. Solve the following equation for x.
2x+1/3 +3=4-(x+2)/2

7. After a 60% reduction, a pair of shoes sold for $30. What was the price of the shoes before the reduction?

8. Solve the following formula for r. I =Prt

9. Simplify the exponential expression. Express your answer with positive exponents. -2x -2y5 (3xy-3)

10. Simplify the exponential expression. Express your answer with positive exponents.
3x-2y2/(2x2y)3

11. For f(x) =2x2-5x =3 and g (x) =x+2 :

a. find (f + g)(x)

b. find (f + g)(2)

12. For f (x) =2x2 -5x+3 and g(x) =x+2 , find f(-2) + g (3) .

13. Use intercepts to graph the linear equation 3x + 5y = 14 . Label the intercepts on the graph.

14. Use the slope formula to find the slope of the line passing through the points

(-3, 7) and (4, -2). Then indicate whether the line through the points rises, fall, is horizontal, or is vertical.

15. Rewrite the equation 3x-4y =12 in slope-intercept form by solving for y. Then give the slope and y-intercept.

16. Find the equation of the line that has a slope of -3 and passes through (2, -5).
Write the equation in slope-intercept form.

17. Find the equation of the line passing through the point (-3, -3) that is perpendicular to the line 2x-y =4 . Write the equation in slope-intercept form.

18. Solve the following system of linear equations by substitution.
2x =3y=7
6x-y=1
Express the solution as a point (x, y). Check your result in both equations.

19. Solve the following system of linear equations by addition.
3x+5y=-17
2x-3y= -5

20. A company is planning to manufacture chairs. The fixed cost is $20,000 and the cost per chair is $40. Each chair will be sold for $80.
a. Write the cost function, C(x), of producing x chairs.
b. Write the revenue function, R(x), from the sale of x chairs.
c. Determine the break-even point. Describe what this means.

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Solution Preview

1. Evaluate [3x-4y]/ 2z when x= -2, y=3, z=4. Express your answer as a fraction.

Insert values and do arithmetic. Note: I rewrote expression [3x-4y] in brackets because that should be done first based on the worksheet you attached. Its that whole expression divided by 2z. As you wrote above it would only have been 3x-(4y/2z) which would have gotten us the wrong answer.

[3(-2)-4(3)]/2(4) = (-6-12)/8 = -18/8 = -9/4

2. Use the order of operations to simplify the following expression. (-2)2 -3 2

PEDMAS - parentheses, exponent, division, multiplication, addition, subtraction
Again referring to the expression in the worksheet
((-2)^2-3^2)/(6/3(2)-2)
(4-9)/(1-2) = -5/-1 = 5

3. Write the following statement as an algebraic equation.

The difference between x and 2 is 4 more than twice x.

difference means subtraction
is means equals

so...
x-2=2x=4

4. Name the property used in the equation: -2 (x+5) =-2x-10
distributive property...you're distributing the -2 into the parentheses

5. Solve the following equation for x. 4(2x-3) +1= 6- 2 (x+4)

distribute the 4 on the left and the -2 on the right
8x-12+1=6-2x-8
combine like terms
10x=9
x=9/10

6. Solve the following equation for x.
(2x+1)/3 +3=4-(x+2)/2

separate fractions
2x/3 +1/3 +3 = 4-(x/2 +2/2)

2x/3 +1/3+3 = 4-x/2-1

Combine like terms
2x/3 +x/2 = -1/3

find common denominator to add fractions
4x/6 + 3x/6 = -1/3

7x/6 = -1/3

cross multiply
x=-6/21 = -2/7

OR
you could find a common denominator to begin with...

7. After a 60% reduction, a pair of shoes sold for $30. What was the price of the shoes before the reduction?

x(.4)=30 (ie 60% reduction is 40% of original price)
x=$75

8. Solve the following formula for r. I =Prt
r=I/Pt

9. Simplify the exponential expression. Express your answer with positive exponents. -2x -2y5 (3xy-3)
You can combine terms with the same base only. So y's can combine and x's can combine. When these terms ...

Solution Summary

The solution assists with explaining how to calculate the given algebraic questions.

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Algebra Questions

See attached file for full problem description.
1. Solve. 6x - 0.37 = 5(x - 0.28)

2. Identify the base in the statment "50% of 300 is 150."

3. Identify the rate in the statment " 260 is 52% of 500."

4. The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs.

5. solve 2/5x = - 10

6. Solve. 4x + 8 = -4

7. solve x/6 + 3 = 9

8. Graph the solution set of x < -4.

9. Is 15 a solution to the equation 8 - x = 7?

10. A home purchased for $300,000 depreciated 8% over a 1-year period. What was the value of the home after at the end of the year?

11. solve for x: 3x - 2y = 6

12. Which label describes the following?
3x + 6 = 10
13. Is 4 a solution to the equation x + 7 = 11?

14. Find two consecutive integers such that the sum of 2 times the first integer and 4 times second integer is 46.

15. solve -3(10x - 3) + 10(3x - 3) = x - 7

16. convert 9/16 to a perect

17. convert 1/2 to a percet

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