Simple Equations and Inequalities | ||
#1 | 7x - 10x = 9 | x= -3 |
#2 | 7x - 9 = -30 | x = -3 |
#3 | A true crab has 4 fewer than twice the number of legs that a hermit crab has. The hermit crab has 6 legs. How many legs does the true crab have? | 8 legs |
#4 | Fiona earns $15 for each lawn she mows. Write and solve an inequality to find out how many lawns she must mow to earn at least $135? | 15m (greater than and equal to) 135; 9 lawns |
#5 | Solve. -6x = 59.8 | x = -9.96 (6 is repeating) |
Multi-Step Equations | ||
#1 | Solve. 8x - 12= -20 | x = -1 |
#2 | Solve. 0.5(8x - 12) = -10 | x = -1 |
#3 | Three times the quantity h + 4 equals four times the quantity h - 1. What value of h makes this true? (Just solve for h). | h = 16 |
#4 | Five times the quantity s + 6 equals three times the quantity s - 2. What value makes this statement true? | s = -18 |
#5 | 10z + 4 = 2(5z + 8) -12 | all real numbers; identity property |
Multi-Step Inequalities | ||
#1 | Solve and Graph. -4z + 8 < -27 + z | z > 7, graph should have an open circle over the 7 and arrow should be going right) |
#2 | 4x > -36 | x > -9 |
#3 | 12 - d > 40 | d < -28 |
#4 | f - 8 < -1.1 | f < 6.9 |
#5 | -6n <(or equal to) 18 | n >(or equal to) -3 |
Writing Equations | ||
#1 | An annual pass for National Park entry costs $80. The total income from the annual passes is $12,800 in one month. Write an equation to represent the situation. | 80p = 12,800 |
#2 | Translate the sentence. The difference of a number and 7 is -8 | n - 7 = -8 |
#3 | Translate. The difference of a number and -7 is -2 | n - (-7) = -2 |
#4 | Translate. Two less than the product of three and a number is -9 | 3n - 2 = -9 |
#5 | Write and Solve. Taylor attached 24 ribbons to a jacket in 4/5 of an hour. At this rate, how many ribbons could he attach in one hour? | 30 ribbons |
Writing Inequalities | ||
#1 | John has a gift card worth $75. If each DVD costs $12.50, how many DVD's can he buy if he spends no more than $75? | Up to 6 DVD's |
#2 | Five times the sum of a number and 15 is greater than 37. | n> 7 3/5 |
#3 | Bradford earns $8 for each car he washes. Write an inequality that can be used to find out how many cars he must wash to earn at least $256. | 8p (greater than and equal to) 256 |
#4 | Translate. Six less than the product of four and a number is less than 0.5 times the opposite of the number. | 4n - 6 < -0.5n |
#5 | Translate. The sum of an integer and the next greater integer is at most 13. Write an inequality to find the lesser integer. Then solve. | n + n + 1 (less than and equal to)13; n (less than and equal to) 6 |
Final Question | |
3x + 2 + 5(x - 1) = 8x + 17 | null set; no solution |