1-Variable
Solve for x:
( - 4/3 ) * x = 12
x = -9
Solve for x:
x + 5 = -2x - 3
x = -8/3
Solve for BOTH x and y:
-4x + 8y = 22
4x + 3y = 33
x = 9/2 or 4 1/2
y = 5
What is the difference between the elimination and substitution methods? Include descriptions of the two methods.
Elimination requires both equations to have one matching x or y coefficient, and it only works for some systems of equations
Substitutions can be used for all systems of equations & it solves for one variable, substitutes that back into an equation, and solves the problem
Show me your drawings goofies.
Solve for x:
4/5x = 3
x = 4/15
10x - 5 = 20x + 10
x = -3/2
Solve for BOTH x and y:
5x + 6y = 17
x = 8y/22
x = 17/8
y = 17/16
Every x-value only has one corresponding y-value.
What is the x-intercept & y-intercept of this equation?
y + 5 = x2 + 1
y-Intercept: (0, -4)
x-intercept: (-2, 0) & (2, 0)
Solve for x:
3(x - 7) = 2x + 10
x = 31
A car travels at 60 miles per hour. How many hours, x, does it take to travel 180 miles?
x = 3
3 hours
Can you find x and y using Elimination?
4y - 4x = 16
12x + 8y = 22
x = - 1/2
y = 7/2
A store sells shoes and socks.
Two pairs of shoes and three pairs of socks cost $84.
Three pairs of shoes and two pairs of socks cost $99.
What is the price of each?
2x + 3y = 84
3x + 2y = 99
Socks (y) cost $10.8
Shoes (x) cost $25.8
How does the distributive property work, and if I give you an expression like the one below, what does it simplify to?
-5x2(10-3x)
-50x2 + 15x3
Solve for x:
(4x)2 + 43 * 3 = (x2 + 8)9
x does not exist, there are no possible answers
Carlos saved $10 each week for x weeks and already had $20. He now has $70. How many weeks has Carlos been saving for?
10x + 20 = 70
Carlos has been saving for 5 weeks
Solve BOTH x and y
3/2 (4x+2y) = 8
2x - (y - 2) = 4
x = 7/6
y = 1/3
Michael is twice Jennifer's age. Six years ago, Michael was three times Jennifer's age. How old is Michael right now?
Michael is currently 24 years old
What is the first arithmetic operation & how did the rest come about/ what's their relationship to the first operation?
Addition was the first
Subtraction is adding negative numbers
Multiplication is repeated addition
Division is multiplying by reciprocals
Solve for x:
(2x-6)/5 + (6x+3)/4 = (5x+7)/2
Hint: What do you do when you want to add fractions with different denominators?
x = -79/12
A gym charges a $25 registration fee and $15 per month for a membership. A different gym charges a $40 registration fee and $12 per month. After how many months will the total cost of both gyms be the same?
15x + 25 = 12x + 40
x = 5 months
Solve for BOTH x and y:
(4x+3y)/2x = 17
3(x+3) - y = 8
x = 1/7
y = 10/7
Dylan has 40 oz. of wax and wants to make 7 candles. A small candle requires 4 oz. while a big candle requires 8 oz. How many small and big candles should Dylan make.
x + y = 7
4x + 8y = 40
Dylan should make 4 small candles and 3 big candles
Simplify this equation:
10 + 4x2 * 2x3 - 3x + 4y - 6 + 9x5
17x5 + 4y - 3x + 4