Solve and Graph
Solve and graph: x+7≥12
x≥5 (closed circle at 5, arrow right)
A taxi charges a $5 base fare plus $2 per mile. You have $35 to spend. Write an inequality to represent the maximum number of miles mm you can travel.
5+2m≤35 or m≤15
3x+8≤29
What values satisfy x−4<2?
Options: 3, 5, 7, 9
x>2 AND x<8
2<x<8
Solve and graph: 2x−5<9
A gym membership costs $40 per month plus a $50 enrollment fee. You want to spend no more than $250. Write an inequality for the number of months nn you can afford.
50+40n≤250 or n≤5
5x−12>18
Which values satisfy 2x+3≥11?
Options: 2, 3, 4, 5, 6
4, 5, 6
Solve: −1<x+3<5
−4<x<2
−3x+4≤−8
x≥4 (closed circle at 4, arrow right)
A catering company charges a $120 setup fee plus $15 per person. Your budget is at most $450. How many people pp can attend?
120+15p≤450 or p≤22
−2x+15≥3
x≤6
Which values satisfy −x+10≤5?
Options: 3, 4, 5, 6, 7
Solve: 4≤2x+2≤10
1≤x≤4
Solve and graph: x/4+3>7
You're buying concert tickets that cost $85 each plus a $12 service fee per ticket. You have $600. Write and solve an inequality for the number of tickets tt you can buy.
t≤6
4(x−3)<20
x<8
Determine the solution set for 5x−20<5x+10:
No Solution, All Real Numbers, x<6, x>6
Two students solve 3<x+1<9.
Student A gets 2<x<8
Student B gets x>2 and x<8
Who is correct and why?
Both students are correct because both inequalities describe the same set of values. The compound inequality can be written as one statement or separated into two parts with "and."
Solve and graph: −5x−10≥15
x≤−5 (closed circle at -5, arrow left)
A food truck charges a $30 delivery fee, $8 per sandwich, and $4 per drink. You order the same number of sandwiches as drinks and want to spend no more than $150. Write an inequality to find how many of each item xx you can order.
x≤10
−3(2x+5)≥9
x≤−4
Determine the solution set for 3x+7≥3x−2
No Solution, All Real Numbers, x≥3, x≤−3
All Real Numbers (the inequality simplifies to 7≥−2, which is always true)
−6≤−2x+4<8
−2<x≤5