Writing and Solving Inequalities

Master inequalities! Write, solve, and graph them with our Grade 9 worksheet. Perfect for algebra practice.

Warm-Up - Take a few minutes to think about each phrase and match it to the correct inequality symbol. > more than exceeding above greater than < fewer than below less than ≥ at least no fewer than minimum no less than ≤ no more than not above does not exceed at most What type of circle does this sign have on a graph? ≥ Open Closed -5x + 5 > 25 x > 4 X < 4 x > -4 x < -4 Select the answer that correctly describes the graph of 3x - 7 ≥ 29 Closed circle at 22 arrow to the right Closed circle at 22 arrow to the left Open circle at 12, arrow to the right Closed circle at 12, arrow to the right Select the answer that correctly describes the graph of -2x - 1 ≥ 3 Closed circle at -2, arrow to the right Closed circle at -2, arrow to the left Open circle at -1, arrow to the right Closed circle at -1, arrow to the right A taxi charges a flat rate of $1.75 plus an addition $0.75 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel? x < 11 x > 11 x < 12 x > 10 Chris is ordering DVDs on Amazon. Each DVD costs $15 and since he isn’t a Prime member, the shipping for the order is going to cost $10. If he can spend no more than $100, how many DVDs could he buy? x < 6 x < 6 x < 10 x < 12 The Mitchell High School choir plans to raise $4,000 for their trip in April, which is 5 months away. They already have $550. What is a reasonable estimate for the amount of money that they must raise each month? x > 600 x < 910 x > 690 x > 900 Stan earned $10.50 per hour taking orders in the drive through. Jamie is trying to make more money than Stan. Jamie makes $6.50 per hour plus an additional $50 tips waiting tables on Saturday evening. Which inequality can be used to find how many hours Jamie has to work to have more than Stan? 6.50+ 50x > 10.50 6.50x + 50 > 10.50x 6.50x + 50 < 10.50x 6.50+ 50x < 10.50 You are learning to play a new instrument. Store A will sell you the instrument for $250 and give lessons for $50 per lesson. Store B has lesson for $100 perlesson and they sell the same instrument for $80. Which inequality can be used to find how many lessons you can take for Store A to be the cheaper deal? 250 + 50x < 100x + 80 250x + 50 < 100 + 80x 250 + 50x < 100 + 80x 250 + 50x > 100x + 80 The perimeter of a trapezoid is at least 25 inches. What inequality represents the possible values of x? x > 12 x > 6 x < 6 x < 6