Elementary Algebra by Denny Burzynski

By Denny Burzynski

Basic Algebra is a piece textual content that covers the conventional subject matters studied in a contemporary hassle-free algebra path. it really is meant for college students who (1) don't have any publicity to undemanding algebra, (2) have formerly had an uncongenial adventure with hassle-free algebra, or (3) have to assessment algebraic innovations and strategies.

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Elementary Algebra

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T✐♣❧② t❤❡ ❢r❛❝t✐♦♥s. 60% ❘❡♣❧❛❝❡ 1 100 ✇✐t❤ t❤❡ % s②♠❜♦❧. 75 ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ 1 100 . 75 · 100 · = 75 · = 75% 1 100 ▼✉❧t✐♣❧② t❤❡ ❞❡❝✐♠❛❧ ❜② ✶✳ 1 100 ❘❡♣❧❛❝❡ 1 100 ✇✐t❤ t❤❡ ✪ s②♠❜♦❧. 623% 1 100 1 100 ◆♦t✐❝❡ t❤❛t t❤❡ ❞❡❝✐♠❛❧ ♣♦✐♥t ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ♥✉♠❜❡r ❤❛s ❜❡❡♥ ♠♦✈❡❞ t♦ t❤❡ r✐❣❤t ✷ ♣❧❛❝❡s✳ ✶✳✽✳✼ ❈♦♥✈❡rt✐♥❣ ❆ P❡r❝❡♥t ❚♦ ❆ ❉❡❝✐♠❛❧ ❲❡ ❝❛♥ s❡❡ ❤♦✇ ❛ ♣❡r❝❡♥t ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ ❞❡❝✐♠❛❧ ❜② ❛♥❛❧②③✐♥❣ t❤❡ ♠❡t❤♦❞ t❤❛t ✶✷✪ ✐s ❝♦♥✈❡rt❡❞ t♦ ❛ ❞❡❝✐♠❛❧✳ ❲❡ ♥❡❡❞ t♦ ✐♥tr♦❞✉❝❡ 1 100 . 12% 1 100 1 100 . = 12 · = 12 100 ▼✉❧t✐♣❧② t❤❡ ❢r❛❝t✐♦♥s.

T❤❡ ♥✉♠❡r❛t♦rs ❛♥❞ ♣❧❛❝❡ t❤❡ s✉♠ ♦✈❡r ✼. = 3+2 7 = 5 7 ❊①❛♠♣❧❡ ✶✳✸✶ 7 9 7 9 − 49 . − 4 9 ❚❤❡ ❞❡♥♦♠✐♥❛t♦rs ❛r❡ t❤❡ s❛♠❡. ❙✉❜tr❛❝t ✹ ❢r♦♠ ✼ ❛♥❞ ♣❧❛❝❡ t❤❡ ❞✐✛❡r❡♥❝❡ ♦✈❡r ✾. = 7−4 9 = 3 9 = 1 3 ✶✳✻✳✽ ❋r❛❝t✐♦♥s ❝❛♥ ♦♥❧② ❜❡ ❛❞❞❡❞ ♦r s✉❜tr❛❝t❡❞ ❝♦♥✈❡♥✐❡♥t❧② ✐❢ t❤❡② ❤❛✈❡ ❧✐❦❡ ❞❡♥♦♠✐♥❛t♦rs✳ ❋r❛❝t✐♦♥s ✇✐t❤ ❯♥❧✐❦❡ ❉❡♥♦♠✐♥❛t♦rs ❚♦ ❛❞❞ ♦r s✉❜tr❛❝t ❢r❛❝t✐♦♥s ❤❛✈✐♥❣ ✉♥❧✐❦❡ ❞❡♥♦♠✐♥❛t♦rs✱ ❝♦♥✈❡rt ❡❛❝❤ ❢r❛❝t✐♦♥ t♦ ❛♥ ❡q✉✐✈❛❧❡♥t ❢r❛❝t✐♦♥ ❤❛✈✐♥❣ ❛s t❤❡ ❞❡♥♦♠✐♥❛t♦r t❤❡ ❧❡❛st ❝♦♠♠♦♥ ♠✉❧t✐♣❧❡ ♦❢ t❤❡ ♦r✐❣✐♥❛❧ ❞❡♥♦♠✐♥❛t♦rs✳ ❚❤❡ ❧❡❛st ❝♦♠♠♦♥ ♠✉❧t✐♣❧❡ ♦❢ t❤❡ ♦r✐❣✐♥❛❧ ❞❡♥♦♠✐♥❛t♦rs ✐s ❝♦♠♠♦♥❧② r❡❢❡rr❡❞ t♦ ❛s t❤❡ ❧❡❛st ❝♦♠♠♦♥ ❞❡♥♦♠✐♥❛t♦r ✭▲❈❉✮✳ ❙❡❡ ❙❡❝t✐♦♥ ❘✳✸ ✭❙❡❝t✐♦♥ ✶✳✹✮ ❢♦r t❤❡ t❡❝❤♥✐q✉❡ ♦❢ ✜♥❞✐♥❣ t❤❡ ❧❡❛st ❝♦♠♠♦♥ ♠✉❧t✐♣❧❡ ♦❢ s❡✈❡r❛❧ ♥✉♠❜❡rs✳ ✶✳✻✳✾ ❙❛♠♣❧❡ ❙❡t ❉ ❋✐♥❞ ❡❛❝❤ s✉♠ ♦r ❞✐✛❡r❡♥❝❡✳ ❊①❛♠♣❧❡ ✶✳✸✷ 1 6 { + 34 .

3 4 ❚❤❡ ❞✐✈✐s♦r ✐s 3 4 4 ✳ ■ts r❡❝✐♣r♦❝❛❧ ✐s 3 . 1 4 3 · 3 1·4 3·3 4 9 = = = ❊①❛♠♣❧❡ ✶✳✷✽ 3 8 3 8 ÷ 54 . ÷ 5 4 ❚❤❡ ❞✐✈✐s♦r ✐s = 3 8 = 3 2·2 2·2·2 · 5 3 · )2 5· )2 )2 · )2 · 2 3·1 2·5 3 10 = = = · 5 4 4 ✳ ■ts r❡❝✐♣r♦❝❛❧ ✐s 5 . 4 5 ✷ ✐s ❛ ❝♦♠♠♦♥ ❢❛❝t♦r✳ ❊①❛♠♣❧❡ ✶✳✷✾ 5 6 5 6 ÷ ÷ 5 12 . 5 12 ❚❤❡ ❞✐✈✐s♦r ✐s = 5 6 = = 5 2·2·3 2·3 · 5 )5 )2 · 2 · )3 · )2 · )3 )5 1·2 1 = 2 = · 12 5 5 12 12 ✳ ■ts r❡❝✐♣r♦❝❛❧ ✐s 5 . ✷✺ ✶✳✻✳✻ ❆❞❞✐t✐♦♥ ❛♥❞ ❙✉❜tr❛❝t✐♦♥ ♦❢ ❋r❛❝t✐♦♥s ❋r❛❝t✐♦♥s ✇✐t❤ ▲✐❦❡ ❉❡♥♦♠✐♥❛t♦rs ❚♦ ❛❞❞ ✭♦r s✉❜tr❛❝t✮ t✇♦ ♦r ♠♦r❡ ❢r❛❝t✐♦♥s t❤❛t ❤❛✈❡ t❤❡ s❛♠❡ ❞❡♥♦♠✐♥❛t♦rs✱ ❛❞❞ ✭♦r s✉❜tr❛❝t✮ t❤❡ ♥✉♠❡r❛t♦rs ❛♥❞ ♣❧❛❝❡ t❤❡ r❡s✉❧t✐♥❣ s✉♠ ♦✈❡r t❤❡ ❝♦♠♠♦♥ ❞❡♥♦♠✐♥❛t♦r✳ ❘❡❞✉❝❡ ✐❢ ♣♦ss✐❜❧❡✳ ❈❆❯❚■❖◆ ❆❞❞ ♦r s✉❜tr❛❝t ♦♥❧② t❤❡ ♥✉♠❡r❛t♦rs✳ ❉♦ ♥♦t ❛❞❞ ♦r s✉❜tr❛❝t t❤❡ ❞❡♥♦♠✐♥❛t♦rs✦ ✶✳✻✳✼ ❙❛♠♣❧❡ ❙❡t ❈ ❋✐♥❞ t❤❡ ❢♦❧❧♦✇✐♥❣ s✉♠s✳ ❊①❛♠♣❧❡ ✶✳✸✵ 3 7 3 7 + 27 .

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