Graphing Simple Inequalities
A student must read more than 10 books to earn a prize. Let x be the number of books read. Write an inequality and graph it.
x>10
x+3≥7
x≥4
3x+2≤11
x≤3
4x−6+2x≤12
x≤3
A pair of shoes costs $50. They are on sale for 20% off, and then a 6% sales tax is added. What is the final price?
$42.40
A diver is below sea level. She is at most 55 feet below sea level. Let x represent her position. Write and graph an inequality.
x≤−55
x−5<10
x<15
4x−6>10
x>4
−3x+5+2x>1
x< 4
A recipe calls for 3/4 cup of sugar for one batch of cookies. If you make b batches and use a total of 47 1/4 cups of sugar, how many batches did you make?
63 batches
A student must complete at least 5 homework assignments to qualify for extra credit. Let x be the number of assignments completed. Write and graph an inequality.
x>5
-2x≤12
x≥6
-5x+5≥25
x≤-4
3(4x-6)-2x≥30
x≥4 4/5
(24 ÷ 3 + 52 − 2 (6 − 4))2 ÷ 4 + 33− 18 ÷ (3 × 3)
235 1/4
A game requires players to choose a number. To qualify for the bonus round, the number must be less than -10 or greater than 3. Let x represent the number a player chooses. Write and graph the inequality.
x < -10 and x>3
x/3>4
x>12
2x−9< 6
x<7.5
−6x+24+9x−12<4x+36
x>24
4x + 7 − 3x + 12 = 2x + 9 + x − 5
x=7 1/2
A number must be greater than -2 and less than or equal to 4 to be included in a special range. Let x be the number. Write and graph an inequality.
−2< x ≤4
-x/2 ≥8
x≤-16
6x+4≤2x+20
x≤4
3x+7−5x+2≤−x−4+2x
x≥ 4 1/3
At an arcade tournament, a player earns points based on performance. On one round, they earn 3 times their base points plus 180 bonus points. On another round, they earn 8 times their base points but lose 270 points due to penalties. Both rounds result in the same total score. Let b represent the player’s base points. Write and solve the equation.
x = 70 base points