Solving Simple Equations
w-1/5=2/5
w=3/5
2(x+2)-7=7
x=5
Two shops each charge a rental fee plus an hourly fee to rent a canoe. How many hours must a canoe be rented for the total costs at both shops to be the same?
Shop A: Rental: $2 Hourly: $5
Shop B: Rental: $8 Hourly: $4
6 hours
abs(2x+6)+1=3
x={-2,-4}
V=lwh
Solve for h
h=V/(lw)
-3b=9
b=-3
6y-8-6-8y=4
y=-9
7-6v=-5-8v
v=-6
The recommended mass m of a baseball is 145 grams. The actual mass is allowed to vary by up to 2 grams. What are the minimum and maximum allowed baseball masses?
minimum=143
maximum=147
Solve the literal equation
5y+8x=-5
for y.
y=(-8x-5)/5
-8q=24
q=-4
-7(x+7)=-56
x=1
-4(x+5)=5(x-4)
No solution
abs(3b+9)-16=5
b={4, -10}
p=2L+2W
W=(P-2L)/2
The difference of 3 times a number and 5 is 13. Write and solve an equation to find the number.
3x-5=13
x=6
4(4m-3)-(m-5)=-52
m=-3
5(x+6)-2x=3(x+10)
infinitely many solutions
Consider the equation
abs(1/6x-3)=x/3
. Without calculating, is x=-6 a solution?
No
The volume of a cone is given by the formula
V=1/3pir^2h
, where r is the radius of the base and h is the height. Solve the formula for h.
h=(3V)/(pir^2)
The measure of the larger angle of an isosceles triangle is four times the measure of each of the other two angles. Find the measure of the larger angle.
120 degrees
s+s+4s=180
4s=120
You order two coffees and a cookie. The cookie costs $2.40. You pay 5% sales tax and leave a $1.75 tip. You pay a total of $11.20. How much does one coffee cost?
$346
4/3=8/(x-1)
x=7
-10abs(h+5)-3=-83
The letters a and b represent nonzero constants. Solve ax-b=30 for x.
x=(b+30)/a