Practice Problems for Algebra
Solve for 4z-7/3-2z= -5
4x-7= -5(3-2z) 4z-7=-15+10z 8=6z z= 8/6= 4/3
x^3 < x2. Describe the possible values of x.
Any non-zero number less than 1.
What is X? (1) x=4y-4 (2) xy=8
Each statement alone is not enough information to solve for x. Using statements (!) and (2) combined, if you substitute the expression for x in the first equation, into the second, you get two different answers. x=4y-4 xy= (4y-4)y=8 4y^2-4y=8 y^2-y-2=0 (y+1)(y-2)=0 y= {-1,2} x= {-8,4}
For each of these statements, indicate whether the statement is True or False: If x^4= 16, then x=2
FALSE: Even exponents hide the sign of the original number, because they always result in a positive value. If x^4= 16, then x could be either 2 or -2.
If -4 is a solution for x in the equation x^2+kx+8=0, what is k?
If -4 is a solution, then you know that (x+4) must be one of the factors of the quadratic equation. The other factor is (x+?). You know that the sum of 4 and 2 must be equal to k. Therefore, k=6.
Determine whether the inequality is True or False. (- 3/4)^3 > -3/4
True: Raising a proper fraction to a power causes that fraction to move closer to 0 on a number line. Raising any negative number to an odd power will result in a negative number.
If x^2+k= G and x is an integer, which of the following could be the value of G-k? A. 7 B. 8 C. 9 D. 10 E. 11
Because you know that x is an integer, x^2 is a perfect square (the square of an integer). Therefore, G-k is also a perfect square. The only perfect square among the answer choices is (C), 9.
For each of these statements, indicate whether the statement is True or False: If x^2= 11, then x= Square root of 11.
FALSE: Even exponents hide the sign of the original number, because they will always result in a positive value. If x^2= 11, then |x|= Square root of 11. Thus, x could be either Square root of 11 or -11.
Determine whether the inequality is True or False. (x+1/x)^-2 > x+1/x, if x>0.
False: Any number x+1/x, where x is positive, will be greater than 1. Therefore, raising that number to a negative exponent will result in a number smaller than 1 whenever x is a positive number.
If |10y-4| >7 and y<1, which of the following could be y? A. -0.8 B. -0.1 C. 0.1 D. 0 E. 1
First, eliminate any answer choices that do not satisfy the simpler of the two inequalities, y<1. Based on this inequality alone, you can eliminate E. Then simplify the first inequality: 10y-4>7 10y>11 y>1.1 The only answer choice that satisfies this equality is A. -0.8
Solve for y: 22- |y+14|= 20
First, isolate the expression within the absolute value brackets. Then, solve for two cases, one in which the expression is positive and one in which it is negative. 22- |y+14|= 20 = 2= |y+14| Case 1: y+14=2 y=-12 Case 2: y+14=-2 y= -16 y= {-16, -12}
If G²<G, which of the following could be G? A. 1 B. 23/7 C.7/23 D.-4 E. -2
If G²<G, then G must be positive (since G² will never be negative), and G must be less than 1, because otherwise G²>G. Thus, 0<G<1. You can eliminate the negative answers in D and E and A is not unless than 1. Therefore only C. 7/23 satisfied the inequality.
Simplify: m^8 p^7 r^12 / m^3 r^9 p x p^2 r^3 m^4
Multiplying exponents = adding Dividing exponents= subtracting m^12 p^9 r^15 / m^3 r^9 p = m^(12-3) p^(9-1) r^(15-9)= m^9p^8r^6
Evaluate: (4+8/2-(-6))- (4+8/2-(-6))
Prioritize Parenthesis (4+8/2+6)- (4+8 /2 +6) = (12/8)= (4+4+6)= 3/2- 14= -25/2 or -12 1/2.
Solve for x and y: y= 2x+9 and 7x+3y=-51
Solve this system by substitution. Sub the value given for y in the first equation into the second equation. Then, distribute, combine like terms, and solve. Once you get a value for x, sub it back into the first equation to obtain the value of y: y= 2x+9 7x+3y=-51 7x+3(2x+9)= -51 7x+6x+27= -51 13x+27= -51 13x=-78 x=-6 Plug back in... y= 2(-6)+9= -3 x= -6: y= -3
For each of these statements, indicate whether the statement is True or False: If x^3= 11, then x= ₃√11.
TRUE: Odd exponents preserve the sign of the original expression. Therefore, if x^3 is positive, then x must itself be positive. If x^3= 11, then x must be ₃√11.
For each of these statements, indicate whether the statement is True or False: If x^5= 32, then x=2.
TRUE: Odd exponents preserve the sign of the original expression. Therefore, if x^5 is positive, then x must itself be positive. If x^5= 32, then x must be 2.
