SOLVE EQUATIONS WITH VARIABLES ON EACH SIDE
WRITE AND SOLVE EQUATIONS WITH VARIABLES ON EACH SIDE
SOLVE MULTI-STEP EQUATIONS
DETERMINE THE NUMBER OF SOLUTIONS
WRITE AND SOLVE MULTI-STEP EQUATIONS

100

WHAT IS THE SOLUTION TO 

3X+4 = 2X +10

X=6

100

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

100

SOLVE

2(X+3)=3X-6

X=12

100

HOW MANY SOLUTIONS DOES 2X+4=2(X+2) HAVE?


INFINITELY MANY

100

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

200

SOLVE FOR X:

5X-2 = 3X+6

X=4

200

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

200

FIND X IN THE EQUATION

3(X-5)+2= X+7

X=10

200

WHAT IS THE NUMBER OF SOLUTIONS FOR 3X+1=3X+5

NO SOLUTIONS

200

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

300

IF 4X+7 = 3X+12, WHAT IS X?

X=5

300

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

300

WHAT IS X IN THE EQUATION

-(4X-8) = 4X-8

X=2

300

DETERMINE THE NUMBER OF SOLUTIONS FOR 4(X-1) = 5X+2

1 SOLUTION

300

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

400

SOLVE THE EQUATION

2(X-3) = 3(X+1)

X=-9

400

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

400

5X+3-2X = 16+2X

X=13

400

DOES THE EQUATION 3(4X-2) = 6(2X+1) HAVE ONE SOLUTION, NO SOLUTIONS, OR INFINITELY MANY SOLUTIONS?

NO SOLUTIONS

400

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


500

WHAT IS THE SOLUTION FOR 

7X+5 = 3X+21

X=4

500

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

500

6(2X-3) = 3(X+3)

X=3

500

HOW MANY SOLUTIONS DOES 5(3X+3) = 5(X+2)+5 HAVE?

1 SOLUTION

500

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

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