65 - week 6 - Algebra I - pg. 66 -83
solve and check this absolute value problem |3x - 4| = 2 possibility that x is (less than or equal to)≤0
-(3x-4) =2 -3x +4 = 2 -3x +4 -4 = 2 -4 -3x = -2 -3x/-3 = -2/-3 x=2/3 check |3(2/3)| -4 = 2 |6/3-4| = 2 |2 -4| =2 |-2| =2
solve this absolute value equation |x + 3|= 5 possibility that x is (less than or equal to ) ≤0
-(x + 3 ) =5 -x -3 = 5 -x -3 + 3 = 5 +3 -x = 8 -x/-1 = 8/-1 x = -8 check |-(-8 +3)| = 5 |8-3| = 5 5=5
simplify -2(-4)(-3)(-3)
-2(-4)(-3)(-3)= 8(9)= 72
Find the value of 7 bananas at 15 cents each.
15 x 7 =? $1.05
Solve for w - A = lw
A = lw A/l = lw/l A/l =w w = A/l
Find the value of (2x +4) stamps at $0.02 each
$0.04x+$0.08
Find the value of y nickels
$0.05y
Find the value of (x+3)folders at $0.10 each
$0.10x+$0.30
Find the value of 6 less than x pens at $1.75 each
$1.75x - $10.50 hint - (you have to find what the 6 pens cost at 1.75 each to know what to subtract)
simplify - (4+3)²- (-5)(-2)=
(4+3)² - (-5)(-2) = 7²-10 49 - 10= 39
Solve the equation for F- C= 5/9(F-32)
C=5/9(F-32) 9/5C=9/5∙5/9(F-32) 9/5C=F-32 9/5C+32 = F-32+32 9/5C=F F =9/5C+32
simplify - I did this so it may not be right! -[2(3-2)][3-(4-8)]
-[2(3-2)][3-(-4-8)] =-[2(1)][3-(-12)] =-2(36) =72
simplify - -[3(4-2)][2-(5-9)]
-[3(4-2)][2-(5-9)] =-[3(2)][2-(-4)] -6(6) =-36
express algebraically - the total cents for x quarters, y nickels, and z pennies
25x +5y +z
express algebraically- The difference between twice a number and the number squared.
2x-x²
Solve and check the absolute value problem- ( you must isolate the absolute value symbol) 2|x+1|-3 =7
2|x+1|-3 =7 2|x+1|-3 + 3 = 7 + 3 2|x + 1|= 10 2|x+1|/2 = 10/2 |x+ 1| = 10 x + 1 =5 or -(x+1) = 5 x + 1 -1 = 5 -1 x =4 -(x+1) =5 -x -1 +1 = 5 +1 -x =6 -x/-1 = 6/-1 x = -6 check both 2|4+1| -3=7 2|5| -3=7 10-3 =7 7=7 2|-6+1|-3 = 7 2|-5|-3=7 10 -3=7 7=7
Solve for s - P = 4s
P = 4s P/4 =4s/4 P/4 = s s = P/4
Solve the formula for p to find the principal. i = $300 r = 16% t = 3 mo. hint - Interest = prt
P = i/rt P = 300/ (16%∙ 1/4) P = 300/ (.16 ∙ .25) P = 300 / .04 P = $7500
Solve the formula for p to find the principal. i = $500 r = 8% t = 1 year hint - Interest = prt
P = i/rt P = 500 / .08∙1 P = 500 / .08 P = $6,250
Solve the formula for r to find the annual interest rate. i = $52 p = $800 t = 6 mo. hint (Interest = prt)
R = i/pt R = 52/ 800∙ 1/2 R = 52 / 800 ∙ .5 R = 52/ 400 R = .13 R = 13%
*Solve the formula for r to find the annual interest rate - i = $2520 p = $7000 t = 3 years
i = prt 2520 = 7000 ∙r ∙3 R = 2520/ 7000 (3) R = 2520 / 21,000 R = .12 R = 12%
Solve the formula for t to find the time- i = $315 p =$1750 r = 9%
i = prt 315 = 1750∙.09∙t T = 315/1750(.09) T = 315/157.5 T = 2
One number is 25% more than another number. The sum of the numbers is 135. What are the two numbers?
x + x + 0.25x=135 2.25x = 135 2.25x/2.25 = 135/2.25 x = 60 check 60 +60 + 15 = 135 (the 15 is from taking 60(.25)
Separate the number 39 into two parts so that the first number is 5 more than the second number. What are the numbers?
x +x+5 = 39 2x + 5 = 39 2x +5 - 5 = 39-5 2x = 34 2x/2 = 34/2 x =17 check - numbers are 17 and 22 17 +22 = 39
Solve this absolute value problem - possibility that x is ≤ 0 |x-3|=5
|x-3|=5 -(x-3)=5 -x +3 =5 -x +3 -3 = 5-3 -x =2 -x/-1 = 2/-1 x = -2 check |-2 -3| = 5 |-5|=5 5=5
Solve this absolute value problem - possibility that x is≥ 0 |x-3|=5
|x-3|=5 x-3=5 x-3+3 =5 +3 x = 8 check - |8-3| = 5 |5|=5 5=5
solve this absolute value problem |3x - 4|= 2 possibility that x is (greater than or equal to)≥0
|3x - 4| =2 3x -4 +4 = 2 + 4 3x = 6 3x/3 = 6/3 x =2 check |3(2) -4| = 2 |6 -4| = 2 2 =2
Solve for x ax + 2a = 3a
ax + 2a =3a ax + 2a - 2a = 3a - 2a ax =a ax/a = a/a x = 1
solve this absolute value equation |x +3| = 5 possibility that x is (greater than or equal to) ≥ 0 (don't forget to check:)
x + 3 = 5 x +3 -3 = 5 -3 x = 2 check |2 + 3| = 5 5 =5
