SOLUTIONS TO ALGEBRA EXERCISES

click a link to go to the solutions on each topic

 A/ Exponents B/ Factoring C/ Rational Numbers (fractions) D/ Equations E/ Inequalities

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 a) b) c) d) e) f) g) a + b h) a² + b² i) a2(1 + b3) j) 1

2) Find a numerical value for the questions in #1 if a = -2 and b = -3.

 a) b) c) d) e) f) g) – 5 h) 13 i) 40 j) 1

3) Simplify the following and find numerical values when possible.

 a) a6 . b) x4 c) 64 d) 27 e) – 35= – 243 f)

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4) Factor completely.

 a) (h + k)(x + y) b) (a + b)(a + b + 2) c) (x – y)(a – b) d) (x + z)(x – y) e) 10x(x – 3)(x + 3) f) 3(1 – 4x)(1 + 4x) g) 2(a – 4b)(a + 4b) h) (2m + p + 8q)(2m – p – 8q) i) (5 – a + b)(5 – a – b) j) (x + 6)(x + 1) k) (a – 12)(a + 2) l) 3(a + 8)(a – 1) m) (5 – 3m)(3 + 2m) n) (5m – 2)(m + 1) o) (8x + y)(x – 4y) p) (9a – 4)(2a + 3) q) 2(x – 2y)(x2 + 2xy + 4y²) r) (a + 5b)(a2 – 5ab + 25b²)

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5) Perform the indicated operations. Reduce to lowest terms.

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6) Perform the indicated operations. Reduce to lowest terms.

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i)

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 a) 3(4x – 1) = 9 – 4x 12x –3 = 9 – 4x 16x = 12 x = ¾ b) 5x – 3(x + 1) = 2(3x + 5) 5x – 3x – 3 = 6x + 10 – 4x = 13 x = – 13/4 c) 15w – 4 = 8w + 31 7w = 35 w = 5 d) 8y2 + 2y –1 = 0(4y – 1)(2y + 1) = 0 y = ¼ or y = – 1/2 e) 4x2 + 5cx – 9c2 = 0(4x + 9c)(x – c) = 0 x = – 9c/4 or x = c f) 2x2 + 2x = 32x2 + 2x – 3 = 0 g) 4x + 5 = 9x2 + 24x + 160 = 9x2 + 20x + 110 = (9x + 11)(x + 1)x = – 11/9 or x = – 1 h) 16x = 144 – 24x + x² x2 – 40x + 144 = 0 (x – 4)(x – 36) = 0; x = 4 or x = 36

 i) 16 = y + 7 so y = 9 j) | 2x – 3 | = 5 so 2x – 3 = 5 or 2x – 3 = – 52x = 8 or 2x = – 2 x = 4 or x = – 1 k) | 5x + 7 | = | 2x – 3 | 5x + 7 = 2x – 3 or 5x + 7 = – 2x + 3 3x = – 10 or 7x = – 4 x = – 10/3 or x = – 4/7 l) 3(x + 4) – 2(5) = 2x + 3 3x + 12 – 10 = 2x + 3 x = 1 m) x + 2 + 7x2 – 14x – 26 = 0 7x2 – 13x – 24 = 0 (7x + 8) (x – 3) = 0 so, x = – 8/7 or x = 3 n) 8a – 32 – a2 + 3a = a2 – 9a + 18 2a2 – 20a + 50 = 0 becomes a2 – 10a + 25 = 0 (a – 5)2 = 0 so a = 5