SOLVE EQUATIONS WITH VARIABLES ON EACH SIDE
WHAT IS THE SOLUTION TO
3X+4 = 2X +10
X=6
GREEN'S GYM CHARGES A ONE-TIME FEE OF $50 PLUS $30 PER SESSION FOR A PERSONAL TRAINER. BREAKOUT GYM CHARGES AN ANNUAL FEE OF $250 PLUS $10 FOR EACH SESSION WITH A TRAINER.
50+30S = 250 +10S
S=10
SOLVE
2(X+3)=3X-6
X=12
HOW MANY SOLUTIONS DOES 2X+4=2(X+2) HAVE?
INFINITELY MANY
MRS. HILL IS DESIGNING A RECTANGULAR VEGETABLE GARDEN FOR HER BACKYARD. THE PERIMETER OF THE GARDEN IS 37 FEET & THE WIDTH OF THE GARDEN IS 11.5 FEET SHORTER THAN TWICE ITS LENGTH. SET UP AN EQUATION TO FIND THE LENGTH OF THE GARDEN AND SOLVE IT
37 = 2L + 2(2L-11.5)
L=10
SOLVE FOR X:
5X-2 = 3X+6
X=4
RYAN'S RENTALS CHARGES $40 FOR ONE DAY PLUS $0.25 PER MILE. ROAD TRIPS CHARGES $25 FOR THE DAY PLUS $0.45 PER MILE
40+0.25M = 25+0.45M
M=75
FIND X IN THE EQUATION
3(X-5)+2= X+7
X=10
WHAT IS THE NUMBER OF SOLUTIONS FOR 3X+1=3X+5
NO SOLUTIONS
THE HALLWAY OF OSCAR'S HOUSE IS IN THE SHAPE OF A RECTANGLE. THE LENGTH OF THE HALLWAY IS 1/2 FOOT LONGER THAN TWICE ITS WIDTH. THE PERIMETER OF THE HALLWAY IS 31 FEET. WRITE AN EQUATION TO FIND THE WIDTH OF THE HALLWAY AND SOLVE IT
31 = 2(1/2 + 2W) + 2W
W=5
IF 4X+7 = 3X+12, WHAT IS X?
X=5
A CONTAINER HAS 130 GALLONS OF WATER AND IS BEING FILLED AT A RATE OF 1/4 GALLON EACH SECOND. ANOTHER CONTAINER HAS 200 GALLONS OF WATER AND IS DRAINING AT A RATE OF 1/3 GALLON EACH SECOND
130+1/4S = 200-1/3S
S=120
WHAT IS X IN THE EQUATION
-(4X-8) = 4X-8
X=2
DETERMINE THE NUMBER OF SOLUTIONS FOR 4(X-1) = 5X+2
1 SOLUTION
MR. MURPHY'S CLASS OF 20 STUDENTS IS GOING ON A FIELD TRIP TO THE SCIENCE CENTER. THE SCIENCE CENTER CHARGES $X PER STUDENT FOR ENTRY AND $2.50 PER STUDENT FOR A 3-D MOVIE. MRS. TODD'S CLASS OF 15 STUDENTS IS GOING TO THE ART MUSEUM. THE ART MUSEUM CHARGES $2.5X PER STUDENTS FOR ADMISSION AND $1 PER STUDENT FOR AN AUDIO TOUR. IF BOTH TRIPS COST THE SAME AMOUNT, WRITE AN EQUATION TO REPRESENT THIS SCENARIO AND SOLVE FOR X
20(X + 2.50) = 15(2.5X + 1)
X=2
SOLVE THE EQUATION
2(X-3) = 3(X+1)
X=-9
BLAKE'S SHIPPING COMPANY CHARGES $7 FOR THE FIRST POUND AND $0.20 FOR EACH ADDITIONAL POUND A PACAKGE WEIGHS. STEVE'S SHIPPING COMPANY CHARGES $5 FOR THE FRIST POUND AND $0.30 FOR EACH ADDITIONAL POUND
7+0.20P = 5+0.30P
P=20
5X+3-2X = 16+2X
X=13
DOES THE EQUATION 3(4X-2) = 6(2X+1) HAVE ONE SOLUTION, NO SOLUTIONS, OR INFINITELY MANY SOLUTIONS?
NO SOLUTIONS
6 FRIENDS WENT TO A BASKETBALL GAME FOR $X DOLLARS A TICKET AND THEN SPENT $8.50 EACH ON SNACKS. A DIFFERENT GROUP OF 4 FRIENDS WENT TO A GAME AND SPENT TWICE AS MUCH FOR TICKETS. THEY ALSO SPENT $6.50 ON SNACKS. WRITE AN EQUATION THAT CAN BE USED TO FIND THE COST OF EACH TICKET & TELL HOW MUCH THE GROUP OF 4 FRIENDS PAID FOR THEIR TICKETS
6(X + 8.50) = 4(2X + 6.50)
$25
WHAT IS THE SOLUTION FOR
7X+5 = 3X+21
X=4
A RECTANGULAR BATHROOM WITH SIDE LENGTHS 6X AND 12X. THE PERIMETER IS EQUAL TO 48X-24; WRITE AN EQUATION THAT REPRESENTS THIS AND SOLVE IT FOR X
(PERIMETER OF RECTANGLE=2L+2W)
2(6X)+2(12X)=48X-24
X=2
6(2X-3) = 3(X+3)
X=3
HOW MANY SOLUTIONS DOES 5(3X+3) = 5(X+2)+5 HAVE?
1 SOLUTION
DECLAN PARTICIPIPATED IN VARIOUS ACTIVITIES LAST WEEK. THE TOTAL NUMBER OF MINUTES HE PARTICPATED IN ALL WAS 5X + 15.75. BELOW IS HOW MUCH TIME HE SPENT ON EACH INDIVIDUAL ACTIVITY.
BIKING: X
SOCCER: 2.5(X + 3) + 2.5
SWIM: 15.5
DOGWALK: 3(X - 13.25)
WRITE AN EQUATION THAT CAN BE USED TO FIND X & HOW MUCH TIME HE SPENT DOGWALKING?
5X+15.75 = X+2.5(X+3)+2.5+15.5+3(X-13.25)
DOG WALKING = 20.25 HOURS