# Algebra Calculations

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.

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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