Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation. Write in lowest terms if necessary. 1) - - 1-20 21 20 2) 1 7 1 6 2 1 2 ) 26-1 100-21 20 1-7 -6 6 - ) 1 - (-1) + + (-) -28 28 8-10 Evaluate the expression. ) 8 - () (-8) 80 100-280 10) Evaluate (x - y) for x = - and y = 6. -87 17,76-2,8-68 Simplify the algebraic expression. 11) (a + 10b) - (10a - 7b) 26a + b 26a + 7b 26a + 17b 6a + 7b Solve the inequality and express the solution set in interval notation. Graph the solution set on the real number line. NOTE: A square bracket, i.e. [, is the same as a filled in circle. A curved bracket, i.e. (, is the same as an open circle. 12) 2x + > 6(6x + ) (-, ) ) -18. + 1.1. 1. -1. -. (-, -] 6) (-1)(-)(-7) -11-2 -21 21 7) 87 0 0 1 87 undefined (-, -) [-, ) 8) -86 divided by - 2 2 - -2
1) -(x + 10) -16x - 2 (2, ) 17) 0. is 1% of a number. Find the number. 626. 0.26 26 62.6 [2, ) (-, 2] (-, 2) Solve the equation. Check your solution. 18) 6x + 1.6 = -.2 {-.8} {-7.2} {-} {-.8} 1) - 1 x = 1 12-2 10 2-10 Solve the problem. ) After a 17% price reduction, a boat sold for $ 21,80. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.) $126,1.18 $2,28.60 20) 7(p + 2) = 8p 7 - $668.60 $26,000 21) t = 6 7 1) A 12-ft. board is cut into 2 pieces so that one piece is 8 feet longer than times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. shorter piece: 1 ft.; longer piece: 11 ft. shorter piece: 2 ft; longer piece: ft. shorter piece: 6 ft; longer piece: 6 ft. shorter piece: 28 ft; longer piece: 6 ft. 16) A rectangular carpet has a perimeter of 26 inches. The length of the carpet is 6 inches more than the width. What are the dimensions of the carpet? 1 by 18 inches 12 by 12 inches 7 by inches 1 by 12 inches - 1 0 7 22) x - 1 = 12 {-1} {7} 1 1 {1} {-7} Evaluate the expression for the given value of the variable. Combine. 2) z2 - z - for z = - 7 27-2) (x + 10x2 + 11) - (x - 7x + 6) -x + 10x2-7x + -x + 10x2 + 7x + -x + 10x2 + 7x + 17 -x + 17x2 +
Multiply. 2) 11x(12x + 2x2 + ) Find the product. Multiply. 26) (x - 8)2 12x8 + 2x2 + 12x8 + 22x7 12x + 22x2 + 12x8 + 22x7 + x x2-80x + 6 x2 + 6 2x2-80x + 6 2x2 + 6 27) (y + x)(y - x) Perform the division. 16y2 + 8xy - x2 16y2-8xy - x2 16y2 - x2 8y2 - x2 28) x 2 + 0x - 11 x 7x - 7x + 6-11 x x + 0-11 x 7x2 + 6x - 11 Simplify the expression. All exponents should be positive integers. 2) (8x2y) -1 (2x2y) 1x0 2x0 2x 1x Perform the indicated computation. Write the answer in scientific notation. 0) (6. 10)(2 10-1) 1.8 108 1.8 10 1.8 107 1.8 108 Perform the indicated computations. Write the answer in scientific notation. 1) 7 10-7 10-1.2 1. x 10. x 10.0 x 10-11 Factor the polynomial completely. If the polynomial cannot be factored, say it is prime. 2) x - 81 (x2 - ) 2 (x2 + ) 2 (x2 + )(x + )(x - ) prime ) xy + 10x - 6y - 60 (x + 10)(y - 6) (y - 10)(x + 6) (x - 10)(y + 6) (y + 10)(x - 6) ) x2 + x - ) - m2 (x - )(x + 1) (x - )(x - ) (x + )(x - ) prime (2 - m)(2 + m) (2 - m)2 (2 + m)2 prime 6) 2x2 + 6 (x - 8)2 prime (x + 8)(x - 8) (x + 8)2 7) 1(a + 12) - y(a + 12) (a - 12)(y - 1) (a + 12)(1 - y) (a + 12)(1 + y) prime 8) x2y - 10xy - 00y y(x - 10)(x + 8) y(x - 10)(x - 8) y(x - 0)(x + 8) y(x + 10)(x - 8)
) x2 - x - 6 (x - 7)(x + ) (x + 7)(x - ) (x - 6)(x + 1) prime 0) 8x2 + 18x + (8x + )(x + ) (2x + )(x + ) (2x - )(x - ) prime 1) 10m - 2mn + 10n (2m - mn + 2n) (-m + 2n) (2m + mn - 2n) prime Evaluate the expression for the given values. 2) m - 2n 2 when m = 2, n = -, and p = -1 8p 1 Simplify the rational expression. ) m 2 - m - 0 0 - m - m + m 2-6 m - 6 m + Perform the indicated operation. Simplify if possible. 21x 7x ) x2 28x x 28 28x 8 28x 18x 2 16 ) 6) 7) 8) y - 2 y + 2 y + 0 y - 0 0 1 x2 x + 6 + 1 x x2 x2-6 6x x + 6 x 2-10x - 16 x2-6 2 0 x + 8 x - 2 x - 2 x + 8 s - t + 12 t - s -8 s - t -16 s - t ) x + 6 x - 7 (x - 7) x(x - 7) x(x - 7) x 2 undefined 0 Simplify the complex rational expression. 1-1 x2 0) 1 2 + 1 x x - 2 2x 2x x + 2 8 s - t (x + 7) x(x - 7) 2x - 7 x + 2 2x 2x x - 2
Solve the equation. 1) 1 + 1 x = 20 x2, - -,, - 1, 1 Solve the rational equation. Check your answer. 7 2) x + 21 + x - 7 = x + 21 x2 + x - 7 {1} { } {0} {-1} Solve the equation for the indicated variable. ) 1 a + 1 b = 1 c for b b = a - c ac b = a + c ac Solve the proportion. ) x + 2 = x - {-6} {6} b = ac a - c b = ac a + c {28} {-28} Given that the pair of triangles is similar, find the missing length. Solve. 6) If apples cost $2.0, how much would 20 apples cost? Solve the problem. $0.0 $0.00 $0.0 $10.00 7) Determine whether the ordered pair (-, ) satisfies the equation x - 6y = -. Yes No 8) If m varies directly as p, and m = 1 when p =, find m when p is. Solve the equation. m = m = 81 m = 2 m = ) x2 = x +, 0, -1, -1, 1 60) 8x + 6x2 + 120x = 0 {0,, } {-, -} {0, -, -} - 1, - ) 12 Simplify the square root. Assume all variables represent positive real numbers. 61) -2 7-10 10-10 10 8 16 x = 16 x = 0 x = 2 x = 2 62) 10x2y 6) xy2 6 x2 6y xy 6 x 6y 10x11 6x x10 x 6 x x11
Simplify the expression. If necessary, express the result that is not a rational number as a decimal rounded to two decimal places. 6) 2 - ()(-1) 1 not a real number Perform the indicated operation and simplify. Assume all variables represent positive real numbers. 6) 6 2 6 2 6 7 22 Graph the inequality. 66) y x + Perform the indicated operation and simplify. Assume all variables represent positive real numbers. 67) 6 2( 6-7) 18 12-2 2 6-2 2 6-7 18 12-7 68) (8 11 + 8) 2 768-128 11 768 + 128 11 712 + 128 11 60 + 128 11 6) 270x 10x7 x 27 x 11 x 110 x8 11
70) ( 7 + )(8 7 + ) 71) 8 7 20 + 0 72 + 2 7 60 7 + 2 00 + 7 7 + 8 7 7-2 7 + 2 + 2 7 + 7 2 Solve the system of equations. 72) y = - x 2 y = x 2-18 (-, 18) (18, ) (2, 1) (18, -) Rationalize the denominator. 10 7) 0 7) 1 + 2 10 10 + 8 + 8 10-8 - 2 Simplify the square root, if possible. 76) 16-/2-6 - 1 1 6 Solve the system of equations. 77) x - y = -2 x + 16y = 0 (, -12) (-12, ) infinitely many solutions no solution Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse. Solve. 78) Two legs of a right triangle measure inches and 10 inches. Find the exact length of the hypotenuse and then find the decimal approximation to the nearest tenth of an inch. 2 7 17.2 in 2 11.8 in 8 in 8 in 7) 2x2-8 = 2 {-, } {-8, 8} {} {-} 80) x2 - x + = 0 {, } { 2, -1} {0, } {-, -} Simplify the expression. 7) 20x7 x2 x x7 x2 x x2 81) x2 + 18x + = 0 {-18 +, -18 - } { +, - } {- + 22, - - 22} { + 22, - 22}
Solve the quadratic equation by any method. 82) (x - )(x + ) = 8 {-, } {-, } {} {-} Graph the solution set of the system of linear inequalities. -x + y - 8) y < - x Solve the quadratic equation by any method. 8) p = 18 + 6 p {1-1, 1 + 1} - 1, + 1 {1 -, 1 + } - - 1 - + 1, 8) 1 2 y 2 = 1 + 1 2 y 1 -, 1 + 2 2 1 -, 1 + 2 2-1 -, -1 + 2 2 no real solution Solve the problem. 86) The sum of three consecutive integers is 87. Find the numbers. 127, 128, 12 12, 10, 11 128, 12, 10 127, 12, 11 87) Twice the sum of a number and - equals 12. Find the number. 0-11 -28 2
88) The length of a rectangular room is 7 feet longer than twice the width. If the room's perimeter is 170 feet, what are the room's dimensions? Width = 26 ft; length = ft Width = 1 ft; length = 6 ft Width = 2 ft; length = 118 ft Width = ft; length = 6 ft 8) The perimeter of a triangle is 8 centimeters. Find the lengths of its sides, if the longest side is 8 centimeters longer than the shorter side, and the remaining side is centimeters longer than the shorter side. 12 cm, 8 cm, 20 cm 12 cm, 8 cm, 2 cm cm, 8 cm, 12 cm 8 cm, 20 cm, 2 cm Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse. 0) Two legs of a right triangle measure inches and inches. Find the exact length of the hypotenuse and then find the decimal approximation to the nearest tenth of an inch. 7 2 7.7 in 7 in 20 in 7 10 22.1 in