Solving Equations
What is the solution to the equation (x+5)/-4 = 3
x=-17
The volume, V, of a box is given by the formula V=lwh, where l is the length, w is the width, and h is the height of the box. What is the result when the equation is solved for h?
h=V/(lw)
What is the smallest integer solution to the inequality 6x+ 2> 2x+ 23
x=6
Ezra heats his home using an oil furnace. At the beginning of the month, his oil tank contained 350 gallons of oil. His furnace was using the oil at a rate of 8.5 gallons per day. Write an equation to determine how many days, d, it will take for the furnace to have 75 gallons left in it?
350-8.5d=75
When solving the equation 5x-7=13, Nina first adds 7 to both sides of the equation. What property justifies this step?
Addition property of equality
What is the solution to the equation (n-3)/5 = -2
n=-7
The circumference, C, of a circle is given by the formula C=2πr, where r is the circle’s radius. If this equation is solved for r the result is?
r= C/(2π)
What is the largest integer solution to the inequality 7x- 31 <3x- 4
x=6
Toni received a $75 gift card to a gas station. Write an equation that could be used to determine the price per gallon of gas if they put 9 gallons in the tank and had $39.45 remaining on the gift card?
75-9g=39.45
Is x=-8 a solution to the equation shown below? Justify your yes/no answer.
(x/2)+7 = (-3x/4)-3
Yes, 3=3
What is the solution to the equation 7(x-1)=2(2x+3)
x=13/3
The area of a shaded region is given by A=16w-30. Solve this equation for w in terms of A
w= (A+30)/16
A hot liquid is placed in a freezer to cool it down faster. The temperature of the liquid, in degrees Fahrenheit, is given by the expression 144-8m, where m is the number of minutes it has been in the freezer. The cook wants to remove the liquid from the freezer when its temperature is at most 50 F. Write and solve an inequality that represents all amounts of times that the liquid can stay in the freezer
m is greater than or equal to 11.75
Two consecutive, even integers have the property that three times the smaller is ten more than twice the larger. If n represents the smaller of the two integers, write an equation that models the information given in this problem
3n=2(n+2)+10
What property was used to take this step
3x+ 12+-15=21
3x+(12+-15)=21
Associative property
What is the solution to the equation 3(2x-1)=4(x+1)
x=7/2
If the equation ax+8=bx+c was solved for the variable x in terms of the constants a, b, and c, the result would be?
x= (c-8)/(a-b)
Emma is driving to see her best friend in another state. The distance she still needs to travel is given by the expression 358-65h, where h is the number of hours she has been driving. She will stop for a break when she has at most 150 miles left to drive. Write and solve an inequality that represents the number of miles she needs to drive before she can stop for a break
h is greater than or equal to 3.2 hours
Two consecutive, odd integers have the property that six more than twice the larger is four times the smaller. If n represents the smaller of the two integers, write an equation that models the given information
2(n+2)+6=4n
Two consecutive, even integers have a sum that is equal to the difference of three times the larger and two times the smaller. What are the two integers?
4 and 6
What is the solution to -2(-x-4)+17= 15-7(x+10)
x=-80/9
What is the result when the equation ax+b=cx+3 is solved for the variable x in terms of the constants a, b, and c?
x=(3-b)/(a-c)
The cook at a local diner made 200 ounces of his famous chili. Each bowl of chili contains 8 ounces. The cook needs to save at least 48 ounces of chili to fill a special pick-up order for a customer. Let n represent the number of bowls of chili that have been sold. Write and solve an inequality to model all possible number of bowls that can be sold while also filling the special pick-up order.
48+8n is less than or equal to 200. n is less than or equal to 19
A cash register holds $1 bills, $5 bills, and $20 bills only. There are nine $1 bills and there are three more $20 bills than $5 bills. There is a total of $344 in the cash register. Let n represent the number of $5 bills in the register. Write an equation that models the information given in the problem using the variable n.
9+5n+20(n+3)=344
A test contains questions worth 1 point, 2 points, and 10 points. There are eight 1-point questions and there are five more 2-point questions than 10-point questions. The test is worth a total of 90 points. Let n represent the number of 10-point questions on the test. Write an equation that models the information given in the problem using the variable n. How many 2-point questions are on the test?
8+2(n+5)+10n=90, 11 2-point questions