By Jane Cook
The first step in complicated math is now the simplest.
Alpha educate your self Algebra I in 24 Hours offers readers with a dependent, self-paced, straight-forward instructional to algebra. it is the excellent textbook significant other for college kids suffering from algebra, a fantastic primer for these seeking to get a head commence on an upcoming category, and a welcome refresher for fogeys tasked with supporting out with homework, all in 24 one-hour classes.
• Algebra is the second-most well known mathematic direction for faculty- sure highschool scholars
• approximately all college-bound highschool scholars now take algebra
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Additional info for Alpha Teach Yourself Algebra I in 24 Hours
31 Hour 3 4. 7 – (–2) = 5 –5 9 –9 a. b. c. d. 5. –8 – (–2) = –6 +6 –10 +10 a. b. c. d. 6. 3 + (–5) + 6 + (–1) = 15 +3 –2 0 a. b. c. d. 7. Review 32 (–2) – 9 + (–3 + 6) – 8 = 0 –11 –16 +16 a. b. c. d. 8. 5 · –3 = 2 –2 +15 –15 a. b. c. d. 9. (–4) · (–2) · 3 · (–1) = +24 –24 +12 –12 a. b. c. d. 10. (–18) ÷ 6 · (–4) ÷ 3 = 8 –4 +4 –8 a. b. c. d. C HAP TE R S UMMAR Y In this hour you will learn about … s )DENTIFYING THE PROPERTIES OF REAL NUM bers s 5SING THE MULTIPLICATION RULE WITH REAL numbers s 5SING THE PROPERTIES OF REAL NUMBERS s 5SING THE DIVISION RULE WITH REAL numbers Now that you know the basic operations of adding, subtracting, multiplying, and dividing positive and negative numbers, in this hour you learn the algebraic properties or rules that go beyond the four opera tions.
Remember that if the numbers being added are positive, the sign of the answer will be positive. If the signs of all the numbers being added are negative, the answer will be negative. Now try these six problems and check your answers on page 30. 1. 2. 3. –6 + –7 = (–5) + –2 = (–1) + (–9) = The problems that follow have more than two negative numbers, but the same rule applies: remove their negative signs, add them, and put the negative sign on the final answer. 4. 5. 6. ” The rule you just learned will work perfectly if all the numbers are positive or all are negative.
B. c. d. e. 2 + 5x + 9 + 3x = 11 + 8x or 8x + 11 –3x + 4 – 2x + (–6) = –5x – 2 or –5x + (–2) (6 – 8) + 7x + 3(x – 4) = –2 + 7x + 3x – 12 = –14 + 10x or 10x – 14 7(n – 2) + 3(5 – n) = 7n – 14 + 15 – 3n = 4n + 1 or 1 + 4n 5(3x – 2) – 3(4x + 3) = 15x – 10 – 12x – 9 = 3x – 19 or –19 + 3x In the previous example e, be sure that the –3 is distributed to the 4x and to the +3, resulting in –12x and –9. In these more complex problems, it is important that you watch all the signs of the numbers very carefully, following the sign rules you learned in Hour 3.
Alpha Teach Yourself Algebra I in 24 Hours by Jane Cook