Solve Inequalities with Positive Multiplication or Division — Examples
Read this topicExplanations 4
- Solving Inequalities: Division Property Much like with normal equations, you can use division to reduce an inequality to a simpler form. Specifically, the division property of i…
By Tommy San Miguel, Tomas San Miguel, Zora Gilbert, Alex Federspiel, Vatsal Ojha, Jonathan Heller, Joshua Siktar
- (Video) Solving 1-Step Inequalities by Friendly Math 101 This video by Friendly Math 101 shows you how to solve one-step inequalities. Summary\large{\text{Summary}}Summary Solvi…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K
- Dividing by a Positive to Solve an Inequality Dividing by a positive to solve an inequality is the same as dividing by a positive to solve an equation. Just remember to divide b…
By Caroline K, Alex Federspiel, Jonathan Heller
- Multiplying by a Positive to Solve an Inequality When we multiply by a positive to solve an inequality, it's the same as multiplying by a positive to solve a regular equation! J…
By Caroline K, Alex Federspiel
Problems 51
- If bbb is a positive constant, solve bx>5bbx > 5bbx>5b for xxx.
- What is the smallest value of xxx such that 7x≥427x \ge 427x≥42?
- If 54x≤5\frac{5}{4} x \le 545x≤5, what is the largest possible value of xxx?
- If 57x≤75\frac{5}{7} x \le 7575x≤75, find the largest possible value of xxx.
- The inequality 2x+4<242x+4<242x+4<24 can be simplified to which of the following?
- Solve 56x>25\frac{5}{6}x \gt 2565x>25.
- Solve 611x>36\frac{6}{11}x \gt 36116x>36.
- Solve 211x>6\frac{2}{11}x \gt 6112x>6.
- If x,l,α,ε>0x, l, \alpha, \varepsilon>0x,l,α,ε>0, solve for yyy in terms of x,l,α,εx, l, \alpha, \varepsilonx,l,α,ε. y2xl<αε2\frac{y}{2xl}<\frac{\alpha\varepsilon}{2}2xly<2αε
- Simplify the inequality 3x>33x > 33x>3.
- Simplify −4<4x<4-4 < 4x < 4−4<4x<4. (Hint: You can divide across the whole inequality.)
- 25x>25y25x>25y25x>25y is the same as saying...
- Consider the multiplication property of equality: "For all real numbers aaa, bbb, ccc, a>ba>ba>b if and only if ac>bcac>bcac>bc." Which of the following conditions must be met i…
- Dividing both sides of an inequality by a positive number doesnt‾\underline{\phantom{doesnt}}doesnt the direction of the inequality.
- Solve −3≤x8-3\leq{\frac{x}{8}}−3≤8x for xxx.
- Which of the following inequalities does the number line above represent?
- What is the inequality a>ba>ba>b equivalent to?
- Solve 212>7x\frac{21}{2}>7x221>7x for xxx.
- x6+3≥12\frac{x}{6}+3\geq{12}6x+3≥12 Which two steps below could be used, in some order, to solve the inequality?
- Which of the following inequalities does the number line above represent?
- If a quadratic equation of the form x2+c=0x^2+c=0x2+c=0 has two real solutions, which of the following must be true of ccc?
- Select the inequalities that can also be expressed as: 4x−8y≥124x-8y \geq 124x−8y≥12
- Which of the following matches the number line above?
- Which inequality below represents the number line above?
- Which of the following matches the inequality graphed on the number line above?
- Above is the graph of an inequality. If the boundary line is y=x+2y = x+2y=x+2 and dotted, which inequality would have this graph?
- A student organization at the University of Pittsburgh is hosting a bake sale. Each of the small desserts are 0.50\0.500.50 (505050 cents) each, but they are being sold in packs…
- Helen recently landed a job that pays 30\3030 per hour. She plans to save at least 1,500\1,5001,500 a month. If her monthly spending is about 930\930930, what's the least amount…
- Alice is selling candles online at her Etsy shop. It costs her about 150\150150 in supplies to make about 800800800 custom and assorted tea light candles of all colors. Alice pl…
- If she wants her net calories to be at most 250250250 calories tonight, and she burns 450450450 calories during her workout, what is the maximum amount of ice cream she can have…
- Janet is moving and wants to turn on the electricity and internet service in her new home. The internet is always a flat fee of 75\7575 per month. The electricity, however, is 0…
- Solve for xxx. (2x+5x)⋅3>42(2x+5x)\cdot 3 > 42(2x+5x)⋅3>42
- Solve for xxx. 8x<200−2x8x<200-2x8x<200−2x
- Valentina is making a bunch of Valentine's Day candy packets to give out on Valentine's Day. She bought a bag of 50 Kisses chocolate and made 50 small double chocolate cookies. …
- If 2x≥1\frac{2}{x} \geq 1x2≥1, what are the possible values of xxx? \\ (Hint: xxx must be positive. Otherwise, 2x\frac{2}{x}x2 would be negative, and less than 111.)
- Solve x2≥12\frac{x}{2} \geq \frac{1}{2}2x≥21 for xxx.
- Solve x2≤22\frac{x}{2} \leq \frac{2}{2}2x≤22 for xxx.
- At most how many 0.50\0.500.50 oranges can you buy with a budget of 4\44?
- Captain Ray plans to buy xxx boxes of ramen, to be split among three of his hungry shipmates (he is generous enough to not take any himself). If he wants each shipmate to get at…
- Simplify the following inequality. 6x<46x < 46x<4
- Simplify the following inequality. 8x≤648x \leq 648x≤64
- Simplify the following inequality. 7x>37x > 37x>3
- Simplify the following inequality. 8x≥188x \geq 188x≥18
- Simplify the following inequality. 11x≤011x \leq 011x≤0
- Simplify the following inequality. 18x<−1818x < -1818x<−18
- Jessica is driving through her neighborhood and sees a poorly made sign that tells her the speed limit for the area is 8x≤2008x \leq 2008x≤200. Jessica has to do some quick math…
- Simplify the following inequality. 5x≤305x \leq 305x≤30
- Which of the following numbers is a solution to the following inequality? 7x≥357x \geq 357x≥35
- Simplify the following inequality. 16x≤216x \leq 216x≤2
- Simplify the following inequality. 100x≥10100x \geq 10100x≥10
- Every hour he asks xxx people this very important question. In an 888-hour work day he will ask a minimum number of 969696 people. What is the minimum number of people he will a…