Writing and Word Problems
Explain why there are either two, one, or no solutions to absolute value equations: WR 18
(y=0) 1 solution; (y=x) 2 solutions;(y =-x) 0 solutions
One fifth of a number is 12. Find the number: WORD 16
1/5x=12--> 1/5x*5=12*5--> x=60
The sum of 19 and 42 and a number is equal to 87. Find the number: WORD 14
19+42+x=87--> 61+x=87--> 61+x-61=87-61--> x= 14
Twice the greater of two consecutive odd integers is 13 less than three times the lesser number. Find the integers: WORD 30
2(x+2)=3x-13--> 2x+4= 3x-13-->2x-2x+4=3x-2x-13--> 4+13=x-13+13--> x=17; x=17, x+2=19
Six less than two thirds of a number is negative ten. Find the number: WORD 23
2/3x-6=10--> 2/3x-6+6=10+6--> 2/3x*3/2=16*3/2--> x=24
Trever is a salesperson who is paid a monthly salary of $500 plus a 2% commission on sales. How much must he sell to earn $2000 this month?: WORD 29
2000=0.02x+500-->2000-500= 0.02x+500-500--> 0.02x= 1500--> x=$75,000 (he must sell $75,00 worth of items)
Twenty nine is thirteen added to four times a number. Find the number: WORD 24
29= 13+ 4x--> 29-13= 13+4x -13--> 16= 4x--> x=4
Three times the greatest of three consecutive even integers exceeds twice the least by 38. Find the integers: WORD 31
3(x+4)= 2x+38--> 3x+12=2x+38--> 3x-2x+12= 2x+38-2x--> x+12-12=38--> x= 26; x=26, x+2=28, x+4=30
Find three consecutive odd integers whose sum is 51: WORD 25
3x+6= 51--> 3x+6-6=51-6--> 3x=45--> x= 15; x=15, x+2=17, x+4=19
Find three consecutive even integers whose sum is -30: WORD 26
3x+6=-30--> 3x+6-6=-30-6--> 3x=-36--> x=-12; x=-12, x+2=-10, x+4=-8
Find four consecutive odd integers whose sum is 8: WORD 28
4x+12=8--> 4x+12-12=8-12--> 4x=-4--> x=-1; x=-1, x+2=1, x+4= 3, x+6=5
Find four consecutive integers whose sum is 94: WORD 27
4x+6=94--> 4x+6-6=94-6-->4x=88--> x=22; x=22, x+1=23, x+2=24, x+3=25
Seven times a number equals -84. Find the number" WORD 15
7x=-84-->7x/7=-84/7--> x=-12
Explain why absolute value can never be negative: WR 17
absolute value represents the distance from zero, meaning that it asks "how far?" rather than "in which direction?" this asks you for the number of units from zero, meaning that both -5 and 5 have an absolute value of 5. this number of units cannot be negative
What is an integer?: WR 2
any number before and after zero not including decimals or fractions
Compare and contrast natural and whole numbers: WR. 1
natural numbers are ahy number after zero (1, 2, 3...) while whole numbers are zero and any number after zero. (natural don't include zero)
Compare and contrast the graphs a<4 and a<_ 4: WR 23
on a number line, these will be graphed in the same place and face the same direction but a< 4 would be closed and a<_4 would be open; on a grpah, they would both be on y axis on point 4 pointing vertically but a<4 would be dotted while a<_4 would be straight
a firefighter spraying water on a fire stood on the middle rung on a ladder. The smoke lessened, so she moved up 3 rungs. It got too hot, so she backed down 5 rungs. Later, she went up 7 rungs and stayed there until the fire was out. Then, she climb the remaining f4rungs and went into the building. How many rungs does the ladder have?: WORD 21
starting on middle= 1 rung up 3,-5,up 7= 5 rungs from middle, up 4= 9 rungs from middle- 9 rungs on each side Total: 9 rungs per side+ middle= 19 rungs
How do you know if two lines are parallel?: WR 22
when each of the lines have the same slope. these lines will never touch
How do you know if two lines are perpendicular?: WR 21
when the second line has a slope that is the opposite reciprocal of the other line's slope. becuase of this, these lines will eventually cross becuase their angles are different
What number increased by -16 is -21?: WORD 11
x+-16= -21--> x+-16+16= -21+16--> x= -5
The sum of a number and -43 is 102. Find the number: WORD 12
x+-43=102--> x+-43+43= 102+43--> x=145
What number decreased by 77 equals -18?: WORD 10
x- 77= -18--> x-77+77=-18-77-->x= -95
What number minus one half is equal to negative three fourths?: WORD 13
x-1/2=-3/4--> x-2/4=-3/4--> x-2/4+2/4= -3/2+2/4--> x= -1/4