1001 Algebra Problems.PDF

Set 22(Page 57) c.The graphs of the lines y= 4 and y= x+ 2 are dashed, so that the inequality signs used in both of the inequal ...

above the line y = 3xand below (or on) the liney = –5. The system of linear inequalities for which the shaded region is the solu ...

none of these systems span the entire Cartesian plane. In fact, it is impossible for such a system of linear inequalities to hav ...

d. (2 – 3x^3 ) – [(3x^3 + 1) – (1 – 2x^3 )] = 2 – 3x^3 – [3x^3 + 1 – 1 + 2x^3 ] = 2 – 3x^3 – [5x^3 ] = 2 – 3x^3 – 5x^3 = 2 – 8x ...

b. –2^2 (2–3– 2–2x^2 ) + 3^3 (3–2– 3–3x^3 ) = –4 21  3 – x^2 + 27 31  2 –  313 x^3  = –4^18 – ^14 x^2 + 27^1 ...

c.First, simplify the left side of the equation: (5x+ 1)(2y+ 2) = 10xy+ 2y+ 10x+ 2 Now, simplify the equation by rearranging a ...

b. –22a^3 bc^2 (d– 2)^3 (1 – e)^2 + 55a^2 b^2 c^2 (d– 2)^2 (1 – e) - 44a^2 bc^4 (d– 2)(1 – e) = 11a^2 bc^2 (d– 2)(1 – e)[–2a(d ...

c. 6 x^2 + 11x– 2 = 6x^2 – x+ 12x– 2 = (6x^2 – x) + (12x– 2) = x(6x– 1) + 2(6x– 1) = (x+ 2)(6x– 1) b. 12 x^2 – 37x– 10 = 12x^2 ...

Set 28 (Page 74) c.First, factor the polynomial: x^2 – 36 = x^2 – 6^2 = (x– 6)(x+ 6) Now, set each of the factors equal to zer ...

d.First, factor the polynomial: 9 –7x– 2x^2 = 9 + 2x– 9x– 2x^2 = 1(9 + 2x) x(9 + 2x) = (9 + 2x)(1 – x) The factors are 9 + 2 ...

Since the inequality does not include “equals,” we do not include those values from the num- ber line that make the polynomial e ...

Since the inequality does not include “equals,” do not include those values from the number line that make the polynomial equal ...

d.Find the x-values that make the expression on the left side equal to zero. Begin by factor- ing the polynomial: x^2 – 9x+ 20 ...

number in each subinterval, and record the sign of the expression above each: Since the inequality includes “equals,” we include ...

values: Form a number line, choose a real number in each of the subinterval, and record the sign of the expression above each, a ...

d. = = = e. 4 xx= ^14 =  250 , provided that xis not zero. b.Any value ofx that makes the denominator equal to zero, even ...

c. - + =   +  = = = = = = a. +  –1 =  –1 =  –1 =  –1 = 2–1= ^12  a. + = + = – = = – = a. - + 1 = – + 1 = ...

b.  =  =  = b.  =   =  = c. (4x^2 – 8x– 5)  = (2x+ 1)(2x– 5)  = (2x+ 1)(2x– 5)[–(2x– 5)] = (2x+ 1) (2x+ ...

d.  – h=  – –  h= h= h= h^1 = d. = = abb+1baa+ 1 = ab a. = = = = 2(6 3 – x) c.  = = = = = = = (x– ...

b.  x 2 2 x^2 + + 4 x x 5  3  2 x x + + 1 ^3 – x+ 2  2 =   – x+ 2  2 =  x x + + 5  1 – x+ 2  2 = – = = ...