TERMINOLOGY
What does infinite # of solutions mean? What is another name for infinite # of solutions?
The equation is true for all values of the variables. Both sides of the equation are identical. Another name is Identity.
7/8 x-5=3 1/6
x = 28/3 or 9 1/3
Solve this:
Write an equation that uses the distribute property on both sides with different coefficients on both sides (does not have a coefficient of +/-1 or zero) and has INFINITELY MANY SOLUTIONS.
ANSWERS VARY.
EX. 4(3x+5)= 2(6x+10)
There are 35 students in Ms. Wesley's 8th grade class. There are 7 more girls than boys. How many boys and girls are in the class?
14 boys and 21 girls
Solve for y:
4.2x - 2y =16.8
y= 2.1x - 8.4
What is a coefficient? Give an example of one.
A number being multiplied by a variable. ( # that is attached to the variable) e.g. 3x and 4n
x+5/8= 9/10
x=11/5 or 2 1/5)
6(4k−6)= −7−8(−3k−5)
-36 does not equal 33. No solution, null set
Max paid $50 to be a member of the Computer Club. When she takes the computer class, it costs him $7. Tony is not a member of the Computer Club, and it costs him $9 for the same class. How many classes would it take for Max's total cost to equal Tony’s total cost?
25 Classes
Sara bought 4 packs of expo markers at a discount of $0.70 per pack. If she paid a total of $17.52, how much was each pack originally?
$5.08 per pack before discount
What does null set mean? Give an example of one.
Another name for No solution or empty set. 3 does not equal 5.
6.5(n + 2.6) = 72.8
n = 8.6
−51 − 6(8k +7) = 4+7(k− 6)
k = -1
The length of the rectangle is 4.7 feet more than the width. If the perimeter of the rectangle is 214 feet, how long is the length of the rectangle?
length is 55.85 feet
6(8x- 6)=4(12x -9)
-36 =-36 infinite # of solutions.
What are the steps when solving equations with variable on both sides?
1. Distribute and combine all like terms on each side of equal sign first. 2. Collect variables on one side of the equation using inverse operations. 3. Collect constants on the other side using inverse operations. 4. Multiply/Divide by the coefficient. 5. Write final answer in x= form.
5(1.2k + 6) = 7.1k+34.4
k = -4
-4x - 2( -3x - 17) = 20
x= -7
Stephanie scores 70, 87, 72 and 85 on her first 4 math quizzes. What does she need to score on quiz 5 so that her average score is a 80?
Score has to be 86 points
1/2x - 4(2x-5)-2=6
x= 1.6 or 1 3/5
What is the difference between an algebraic expression and an equation?
Algebraic expressions has variables, variables with numbers and operations. It has no equal sign. Equations have equal signs.
27 / 3(n-3) = 12
n = 3 3/4
−6(3 + x) - (7x − 2) = −6 + 2x
x = -2/3
A cell phone company charges a $27.95 monthly fee and $.12/min for local calls. Another company charges $12.95 a month and $.32/min for local calls. For what number of minutes of local calls are the costs of the plans the same?
75 minutes
John runs a total of 50 miles for 4 days a week. On Monday he ran 4 miles less than Tuesday. On Tuesday he ran half the amount of Wednesday. On Thursday he ran 3 miles more than on Monday. How many miles did he run each day?
M- 7 miles, T- 11 miles, W- 22 miles, and Th- 10 miles.