Solving Equations and Inequalities

Solving Equations

100

2x - 8 = 4

x=6

200

6x + 29 = 53

x=4

300

-8 + x = -5

x = 3

Solving Inequalities

100

3x+3<9

x < 2

200

-x+5 < -10

x > 15

300

(m/-6)+16  > 19

m <-18

Equations from Story Problems

100

Switch Gears Activity Boxes sends a new building activity in the mail each month. Derek prepaid an 8-month subscription for his daughter. He signed up during their holiday sale and received $15 off the total cost. Derek paid $81 in all. Which equation can Derek use to find x, the regular cost per month? 

8x - 15 = 81

x = 12

200

Riley and her friends went to the Color Splat paint-tag course last weekend. The course charges $40 for an hour of group tag plus a rental fee for each paint marker. Riley's group played for one hour, rented 6 paint markers, and paid a total of $94.Which equation can you use to find the rental fee, x, for each paint marker? 

6x+40=94

x = 9

300

Mr. Mosley ordered pizzas for the volunteers at Highland School's fundraiser event. He ordered 12 large pizzas from the Roman Rounds pizzeria. Since this was a bulk order, Roman Rounds reduced the price of each large pizza by $2. The total came to $192.Which equation can you use to find the amount of money, p, Roman Rounds normally charges for a large pizza? 

12(p-2) = 192

p = 18

Inequalities from Story Problems

100

The difference between a number and 7 is greater than -23

x-7 > -23

x>-16

200

Eight more than the quotient of a number and -5 is less than or equal to 6.

(x/-5) + 8≤ 6

x ≥ 10

 

300

14 more than twice a number is at most 50.

2x - 14 ≤ 50

x ≤ 32