Equations - Overview
1 and 2 step
Variables on Both sides
Literal Equations
?????
100
The goal in solving equations is to _______ the variable
Isolate the variable
100
x-13=-27
x=-14
100
The solution to an equation 2x+3 = 2x+3
Infinite solutions - the Identity equation
100
A literal equation is____
Equation with more than one variable
100
Tommy has $25.60. He spent some money and now he has $15. Write an equation to represent the amount of money, m, Tommy spent, then solve for m
25.60 - m = 15 m = $10.60
200
To check a solution for an equation:
Plug it back in and see if it works!
200
5+2x=-3
x=-4
200
Buddy is solving an equation. He does the same operation to both sides and ends up with an equation 2 = -4. What is the solution to his equation?
No solution
200
Solve the equation for y 2y + xy = h
y = h/(2+x)
200
7 = (x-8) / 3
x = 29
300
1/3 + 5/7 =
22/21
300
(1/2)(-4x-6)=-5
x=-1
300
2(a-4)=4a-(2a+4) Be careful simplifying the second part! Not 4a times 2a + 4 distribute the negative!
No solution
300
Solve for x A = Bxt + fh
x = (A - fh)/(Bt)
300
Two friends are renting an apartment. They have to put a security deposit of $500 down and pay the first two months rent. The total check they give their landlord is $2800. What is the rent for one month?
$1150
400
1 and 1/2 times 4 and 2/3 =
7/3 or 2 and 1/3
400
(1/5)t - 3 = -17
t = -70
400
32-40d=23d+30
2/63
400
The formula for the volume of a cylinder is V = pi (r^2) h. Where r is the radius and h is the height. Solve the equation for h. What is the height of a cylinder with a volume of 415.6in^3 and radius of 5 in?. (Use 3.14 for pi.)
5.294 in tall.
400
[(x-7)/3]+12 = (1/2)(4x-6)
x = 38/5
500
One Taxi company charges $0.10 per mile plus a base fee of $15. Another Taxi service charges $0.15per mile plus a base fee of $10. How many miles must you travel to pay the same amount at either company?
100 miles
500
(2/3) + (3/5)m = 31/15
x=7/3
500
3(1/2 + 1/5x) = 17/2 + 4/5x - 4
x = -15
500
A park in the shape of a rectangle with a semicircle on top is 20ft wide. Its total area is 957 ft^2. How long is the park? (Use 3.14 for pi)
40 ft
500
(4/3)x + (4/6)((x/3)+ (2/3)) = (5/3)((9x/3) - 1/3)
x= -9
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