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