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Questions and Answers
Solve the equation: -8x - 7x = 30.
Solve the equation: -8x - 7x = 30.
-2
Solve the equation: Enter a number answer only. Round any decimal answer to the nearest hundredth.
Solve the equation: Enter a number answer only. Round any decimal answer to the nearest hundredth.
64
Solve the equation: 3.5x - 15 = -22.
Solve the equation: 3.5x - 15 = -22.
-2
Solve the equation: -35 = 5(t - 4).
Solve the equation: -35 = 5(t - 4).
Solve the equation: 3(x + 5) = 27.
Solve the equation: 3(x + 5) = 27.
Solve the equation: 6(-3r + 4) = 24.
Solve the equation: 6(-3r + 4) = 24.
Solve the equation: 4x + 12.7 = 32.7.
Solve the equation: 4x + 12.7 = 32.7.
Solve the equation for b: -18 + 8b = 7(b - 4) + 5.
Solve the equation for b: -18 + 8b = 7(b - 4) + 5.
Solve the equation for m: -10m + 36 = 2(-m + 2).
Solve the equation for m: -10m + 36 = 2(-m + 2).
Solve the equation for x: -1 - (7x + 5) = 10 - 3x.
Solve the equation for x: -1 - (7x + 5) = 10 - 3x.
Solve the equation for b: 7(b - 2) = -19 + 6b.
Solve the equation for b: 7(b - 2) = -19 + 6b.
Solve the equation for p: 10 - 7p = -(8p - 5).
Solve the equation for p: 10 - 7p = -(8p - 5).
Solve the equation: -8x - 5 = -6x + 25.
Solve the equation: -8x - 5 = -6x + 25.
Solve the equation: 9x - 7 = -4x - 46.
Solve the equation: 9x - 7 = -4x - 46.
Solve the equation: 9 - 15x = 28 + 4x.
Solve the equation: 9 - 15x = 28 + 4x.
Solve the equation: 3x - 7 = 5x + 1.
Solve the equation: 3x - 7 = 5x + 1.
Solve the equation: 5x + 2 = -x + 14.
Solve the equation: 5x + 2 = -x + 14.
Solve the inequality for x: -20x + 36 > -4(4x - 5).
Solve the inequality for x: -20x + 36 > -4(4x - 5).
Solve the inequality: 2x - 5 > 7.
Solve the inequality: 2x - 5 > 7.
Determine the cost equation: An electrician charges a fee of $45 plus $30 per hour.
Determine the cost equation: An electrician charges a fee of $45 plus $30 per hour.
Express Mary's gross profit (P) as a function of the number of (x) items sold: She earns $390 base pay plus $33 per item.
Express Mary's gross profit (P) as a function of the number of (x) items sold: She earns $390 base pay plus $33 per item.
Express Mary's gross profit (P) as a function: She earns $420 base pay plus $45 per item sold.
Express Mary's gross profit (P) as a function: She earns $420 base pay plus $45 per item sold.
What is the number if -16 is added to it and the sum is doubled to equal 17 less than the number?
What is the number if -16 is added to it and the sum is doubled to equal 17 less than the number?
How many copies must be made for Company A to be more expensive than Company B?
How many copies must be made for Company A to be more expensive than Company B?
What score does Allie need to average 260 after 5 games?
What score does Allie need to average 260 after 5 games?
Find the small integer if the difference between a small and large integer is 28 and the large is three times the small.
Find the small integer if the difference between a small and large integer is 28 and the large is three times the small.
How old am I if 100 increased by 4 times my age is 132?
How old am I if 100 increased by 4 times my age is 132?
What does Sean need to bowl in his 5th game to average 245?
What does Sean need to bowl in his 5th game to average 245?
Evaluate the function g(x) = 2x + 5; Find g(-5).
Evaluate the function g(x) = 2x + 5; Find g(-5).
Determine the range of the set {(-3, 4), (4, 4), (3, 4)}.
Determine the range of the set {(-3, 4), (4, 4), (3, 4)}.
Which relation is a function?
Which relation is a function?
Find f(4) when f(x) = x^2 - 3x + 3.
Find f(4) when f(x) = x^2 - 3x + 3.
Find the slope of the line through the points (-14, 10) and (-3, 15).
Find the slope of the line through the points (-14, 10) and (-3, 15).
Find the slope of the line through the points (-8, -2) and (2, -9).
Find the slope of the line through the points (-8, -2) and (2, -9).
Find the slope of the line through the points (-2, 6) and (10, -5).
Find the slope of the line through the points (-2, 6) and (10, -5).
Would the number of visitors at Rocky Mountain National Park be a dependent or independent variable?
Would the number of visitors at Rocky Mountain National Park be a dependent or independent variable?
Find the slope of the line represented by the equation x - y = -1.
Find the slope of the line represented by the equation x - y = -1.
Find the slope of the line represented by the equation 3x - 5y = 0.
Find the slope of the line represented by the equation 3x - 5y = 0.
Is the slope of the line y = -2x + 3 positive, negative, zero, or undefined?
Is the slope of the line y = -2x + 3 positive, negative, zero, or undefined?
Is the slope of the line x = 10 positive, negative, zero, or undefined?
Is the slope of the line x = 10 positive, negative, zero, or undefined?
What is the x-intercept on the graph of y = -2/3x + 8?
What is the x-intercept on the graph of y = -2/3x + 8?
What is the x-intercept on the graph of the equation 3x + 6y = -18?
What is the x-intercept on the graph of the equation 3x + 6y = -18?
What is the y-intercept on the graph of the equation 4x + 8y = -24?
What is the y-intercept on the graph of the equation 4x + 8y = -24?
Write the standard form of the equation for the line y = -3x - 5.
Write the standard form of the equation for the line y = -3x - 5.
If a school orders an unknown amount of boxes of 15 pens and 3 packages of 6 pens for a total of 288 pens, how many boxes were ordered?
If a school orders an unknown amount of boxes of 15 pens and 3 packages of 6 pens for a total of 288 pens, how many boxes were ordered?
If a cab company charges a $6.00 fee plus $0.20 per mile, how many miles did you go if the fare was $9.40?
If a cab company charges a $6.00 fee plus $0.20 per mile, how many miles did you go if the fare was $9.40?
What was the rate of growth per month in inches if a tree grows from 24 inches to 60 inches in 6 months?
What was the rate of growth per month in inches if a tree grows from 24 inches to 60 inches in 6 months?
What is the profit from selling 23 T-shirts after investing $150 and selling each for $8.25?
What is the profit from selling 23 T-shirts after investing $150 and selling each for $8.25?
If Kristina spends $85 on gift cards, buying 2 cards worth $15 each, how many $20 restaurant cards can she buy?
If Kristina spends $85 on gift cards, buying 2 cards worth $15 each, how many $20 restaurant cards can she buy?
What is the profit from selling 26 T-shirts after investing $180 and selling each for $10.25?
What is the profit from selling 26 T-shirts after investing $180 and selling each for $10.25?
If a car rental company charges $30 plus $0.45 per mile, how many miles did you drive if you paid $61.95?
If a car rental company charges $30 plus $0.45 per mile, how many miles did you drive if you paid $61.95?
To rent a cabin, if a resort charges $84 plus $9.75 per person, how many people used it if you spent $142.50?
To rent a cabin, if a resort charges $84 plus $9.75 per person, how many people used it if you spent $142.50?
What is the coefficient in the monomial -4x^5?
What is the coefficient in the monomial -4x^5?
What is the exponent in the monomial 9b^2?
What is the exponent in the monomial 9b^2?
What is the exponent in the monomial -4x^5?
What is the exponent in the monomial -4x^5?
Add: 5a^2b + 7ab^2.
Add: 5a^2b + 7ab^2.
Subtract: 5x^7 - (-4x^7).
Subtract: 5x^7 - (-4x^7).
How many more SUVs were sold than convertibles?
How many more SUVs were sold than convertibles?
Write the perimeter expression for a rectangle with length 2x and width 3x + 2.
Write the perimeter expression for a rectangle with length 2x and width 3x + 2.
How many more SUVs than convertibles were sold over 3 months?
How many more SUVs than convertibles were sold over 3 months?
How many SUVs were sold in 3 months?
How many SUVs were sold in 3 months?
If Adam bikes for 3 hours and calculates his distance with a polynomial, how far will he have gone?
If Adam bikes for 3 hours and calculates his distance with a polynomial, how far will he have gone?
What type of sequence does Jaycee's can collection represent?
What type of sequence does Jaycee's can collection represent?
Write the sixth term of the sequence represented by 4n + 5.
Write the sixth term of the sequence represented by 4n + 5.
Write the thirteenth term of the sequence represented by 6n - 2.
Write the thirteenth term of the sequence represented by 6n - 2.
Write an explicit rule for the following sequence: 7, 13, 19, 25, 31,...
Write an explicit rule for the following sequence: 7, 13, 19, 25, 31,...
Write an explicit rule for the following sequence: 8, 3, -2, -7, -12,...
Write an explicit rule for the following sequence: 8, 3, -2, -7, -12,...
What is the rule for the nth term of the arithmetic sequence 8, 19, 30, 41, 52,...?
What is the rule for the nth term of the arithmetic sequence 8, 19, 30, 41, 52,...?
What is the rule for the nth term of the arithmetic sequence -5, -2, 1, 4, 7,...?
What is the rule for the nth term of the arithmetic sequence -5, -2, 1, 4, 7,...?
Solve the system by graphing: y = -0.5x + 4; y = x + 3.
Solve the system by graphing: y = -0.5x + 4; y = x + 3.
Solve the system by graphing: y = 2x - 7; y = -3x + 8.
Solve the system by graphing: y = 2x - 7; y = -3x + 8.
What is the solution to the system of equations: x + 3y = 7; 2x + 6y = 15?
What is the solution to the system of equations: x + 3y = 7; 2x + 6y = 15?
Identify the solution for the system 6x - 10y = 4; x + y = 14.
Identify the solution for the system 6x - 10y = 4; x + y = 14.
Study Notes
Equations and Solutions
- Solving linear equations often yields single numerical results. Examples include:
- From -8x - 7x = 30, the solution is -2.
- For the equation 3.5x - 15 = -22, the solution is -2.
- The solution for -35 = 5(t - 4) is -3.
- To find x in equations like 9 - 15x = 28 + 4x, the solution is deduced to be -1.
Solving Inequalities
- Inequalities can also be solved, yielding ranges. For instance:
- From the problem 2x - 5 > 7, the solution is (6, ∞).
- Another inequality results in (5, ∞) from the equation -20x + 36 > -4(4x - 5).
Function Expressions
- Functional relationships can be expressed in terms of variables:
- Electrician charges: y = 30x + 45 where y is cost and x is hours.
- Gross profit for Mary: P(x) = 33x + 390, depending on the items sold.
Age and Profit Problems
- Age problems can be framed into equations; for example, if 100 increased by 4 times my age is 132, my age is found to be 8.
- Profit calculations require initial investment and sales prices. Selling 23 T-shirts after investing $150 yields a profit of $39.75.
Sequences and Series
- Sequences show consistent patterns. For example:
- The sequence 8, 3, -2 can be expressed as an explicit rule: -5n + 13.
- Understanding sequences helps determine values such as the 6th term in 7n + 5 which is 29.
Systems of Equations
- Systems can often be solved visually or algebraically. For example:
- The intersection of y = -0.5x + 4.5 and y = x + 3 results in the point (1, 4).
Slope and Line Analysis
- The mathematical slope informs us about line behavior:
- The slope of y = -2x + 3 is negative.
- Parallel lines maintain consistent slopes, while perpendicular lines have slopes that are negative reciprocals of each other.
Graphical Intercepts
- Finding intercepts provides crucial points on a graph:
- The x-intercept of y = -2/3x + 8 is (12, 0).
- Conversely, the y-intercept of 4x + 8y = -24 is (0, -3).
Arithmetic and Algebraic Calculations
- Routine arithmetic operations involving polynomials can simplify expressions, such as:
- Subtracting 5x^7 - (-4x^7) yields 9x^7, showcasing the use of the distributive property.
Coefficient and Exponent Identification
- Fundamental terms in algebra include identifying coefficients and exponents:
- In the monomial -4x^5, the coefficient is -4 and the exponent is 5.
Real-World Applications
- Many scenarios employ mathematical principles, from calculating rental costs to determining payments based on mileage. For instance:
- A cab fare of $6 plus $0.20 per mile leads to a total fare of $9.40 for 17 miles.
Systems Solved by Elimination and Substitution
- Solving using different methods offers varied insights. For example:
- A substitution method yields (2,1) in the system of equations 6x - y = 11 and y = -8x + 17.
Final Conclusions
- Linear systems can lead to unique solutions, infinitely many solutions, or no solutions, showcasing the variety in equation outcomes.
Studying That Suits You
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Test your knowledge with these Algebra 1 final flashcards. Each card presents an equation for you to solve, ensuring you can apply your understanding of algebraic concepts. Get ready to hone your skills and prepare for your final exam!
