Numbers and Algebra - Operations - Quiz 2
Which expression can be used to solve the following word problem? Mrs. Bussey has planned a field trip for the third grade students. They have 2 buses and 49 people that need rides. There are also 2 coolers that will carry the lunches that need to be stored on the bus. On the morning of the field trip, 3 students are absent. How many people will be on each bus?
(49−3)/2 First, 49 people needed rides but then 3 students were absent, leaving 46 people needing a ride. Since there are 2 buses, there will be 23 on each bus.
Solve: [-4(3-5) + 2]/{-3[3+ 7(4)] + 8}
-2/17 [-4(3-5) + 2]/{-3[3+ 7(4)] + 8} = (-4(-2) + 2) / (-3(31) + 8) = (8 + 2)/(-93 + 8) = 10/-85 = -2/17
If 6(3x+4) = 2(x+2) - 8, what is the value of x?
-7/4 Using distribution, 6(3x + 4) = 2(x+2) - 8 becomes 18x + 24 = 2x + 4 - 8. Combining like terms yields the equation 18x + 24 = 2x - 4. Subtracting 24 and 2x from both sides yields 16x = -28. Dividing both sides by 16 yields x = -28/16 which reduces to -7/4.
Solve: [7(3 - 1)2 + (-8)]/{-3[3+ 6(½)] + 19}
20 [7(3 - 1)2 + (-8)]/{-3[3+ 6(½)] + 19} = [7(2)2 + (-8)] / {-3[3+ 3)] + 19} = [7(4) + (-8)] /{ -3(6) + 19}= [28 + (-8)] / {-18 + 19} = 20/1 = 20
Simplify the expression: 3x + 2(3x - 2) + 5 - 2(2x + 1)3x+2(3x-2)+5-2(2x+1)
5x-1 First, each value from the front of each set of parentheses must be distributed into the parentheses and multiplied appropriately, with attention to positive and negative signs: 3x + 6x - 4 + 5 - 4x - 23x+6x-4+5-4x-2. Next, like terms must be collected to be combined: (3x + 6x - 4x) + (-4 + 5 - 2)(3x+6x-4x)+(−4+5-2).
Which of the following correctly simplifies the left side of the equation below? 3x - 4 + 6x + 5 - 4x - 2 = 16
5x - 1 = 16 This is the only answer option that combines the terms correctly. Another way to write the problem is 3x + 6x - 4x - 4 - 2 + 5 = 16; this can then be written 5x - 1 = 16.
Which of the following options shows a logical and correct first step to solving the algebraic equation given? 3(2x + 1) - 5(x + 4) = 113(2x+1)−5(x+4)=11
6x + 3 - 5x - 20 = 116x+3−5x −20=11 The equation 3(2x + 1) - 5(x + 4) = 11 is best approached by distributing the values from outside of the parentheses into each set of parentheses. It is important to note that the 3 distributed into the first set of parentheses is a positive 3 and so will not change the signs of the quantities it is multiplied with. However, the quantity following that first set of parentheses shows that 5 times a quantity will be subtracted. Therefore, the 5 distributed into the second set of parentheses is a -5, which will change the sign on the x and the +4. Therefore, the left side of the equation becomes: 3(2x + 1) - 5(x + 4) = 3(2x) + 3(1) - 5(x) - 5(4), which results in the equation becoming 6x + 3 - 5x - 20 = 11.