Solve 5x + 3 = 2x + 18.
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Answer
x = 5
Subtract 2x: 3x + 3 = 18. Subtract 3: 3x = 15. Divide: x = 5. Check: 28 = 28.
Algebra Workout
Equations, factoring, functions and logs, solved step by step
Algebra Workout is a Bertopia flashcard pack of 62 cards: equations, factoring, functions and logs, solved step by step. It covers linear equations; inequalities and absolute value; systems of equations; lines and coordinates; polynomials and factoring; quadratics; exponents; radicals and rational equations; functions; exponentials and logarithms; sequences and series; complex numbers.
Sample cards
Solve −3x + 4 > 19.
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Answer
x < −5
−3x > 15. Dividing by a negative flips the sign: x < −5. Check x = −6: 18 + 4 = 22 > 19.
Solve x + y = 10 and x − y = 4.
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Answer
x = 7, y = 3
Add the equations: 2x = 14, so x = 7 and y = 3.
What is the slope of the line through (2, 5) and (6, −3)?
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Answer
−2
(−3 − 5)/(6 − 2) = −8/4 = −2.
Expand (x + 3)².
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Answer
x² + 6x + 9
(x + 3)(x + 3) = x² + 3x + 3x + 9. Squares do not distribute over addition, so x² + 9 is wrong.
Solve x² − 5x + 6 = 0.
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Answer
x = 2 or x = 3
(x − 2)(x − 3) = 0. Check: 4 − 10 + 6 = 0 and 9 − 15 + 6 = 0.
Sources
2 sources
- OpenStax, College Algebra 2e, OpenStax, Rice University
- OpenStax, Elementary Algebra 2e, OpenStax, Rice University
