Solving Inequalities by Grouping - Examples & Practice
Read this topicExplanations 3
- (Videos) Solving Linear Inequalities with Variables on Both Sides by PatrickJMT This video by Patrick JMT goes through an example inequality with variables on both sides. Summar…
By Ben Ferrara, Zora Gilbert, Alex Federspiel, Vatsal Ojha, Amy Feraco, Jonathan Heller, Anusha Rahman
- Solving Inequalities by Grouping There are two things we need to do to solve inequalities with variables on both sides: simplify and isolate. That is, reduce anything we can, an…
By Hannah Bonville, Zora Gilbert, Vatsal Ojha, Jonathan Heller, Caroline K, Anusha Rahman
- Solving Inequalities: Grouping When tackling linear inequalities, there are two simple steps to follow. First, simplify. Then, isolate the variable. Let's look at a practice pro…
By Anusha Rahman
Problems 21
- Solve for xxx if 7x−5<97x-5 < 97x−5<9.
- Solve for xxx if 2x−6>182x-6 > 182x−6>18.
- Solve for xxx. x−(−2x)+8<20−xx-(-2x)+8<20-xx−(−2x)+8<20−x
- Solve for xxx. 3(x−4)+x−2(x+1)≤8(x+x)−x(2(2x−(x+x)))3(x-4)+x-2(x+1)\leq 8(x+x)-x(2(2x-(x+x)))3(x−4)+x−2(x+1)≤8(x+x)−x(2(2x−(x+x)))
- If xxx satisfies 2x−(1−8)−(−6−8)+(1−4)≤x+(1+7)−(6+(−7)),2x-(1-8)-(-6-8)+(1-4)\leq x+(1+7)-(6+(-7)),2x−(1−8)−(−6−8)+(1−4)≤x+(1+7)−(6+(−7)), what's the largest number xxx can be?
- Solve for xxx. 4(2−x)<3(4−2x)4(2-x)<3(4-2x)4(2−x)<3(4−2x)
- Solve for xxx. 4(x−2)−8(2−x)>14(3−x)+7(2x+8)4(x-2)-8(2-x)>14(3-x)+7(2x+8)4(x−2)−8(2−x)>14(3−x)+7(2x+8)
- Which values of xxx below satisfy the following inequality? 6(6x+6)<6(6−6x)6(6x+6)<6(6-6x)6(6x+6)<6(6−6x)
- Solve for xxx. 4(x+6)−3(x−1)<5(2x+9)4(x+6)-3(x-1)<5(2x+9)4(x+6)−3(x−1)<5(2x+9)
- Solve for xxx. 8(6−x)>2(5x−13)8(6-x)>2(5x-13)8(6−x)>2(5x−13)
- Solve for xxx. 14−3(x−9)<22x−5(3x+1)14-3(x-9)<22x-5(3x+1)14−3(x−9)<22x−5(3x+1)
- Solve for xxx. 4(6x+8)<5(7x+2)4(6x+8)<5(7x+2)4(6x+8)<5(7x+2)
- Solve for xxx. 8(x+8)>(5x−2)−3(4x−3)8(x+8)>(5x-2)-3(4x-3)8(x+8)>(5x−2)−3(4x−3)
- Solve for xxx. −(x+9)<−4(−4x+9)−4(−3)+5(9x+6)-(x+9)<-4(-4x+9)-4(-3)+5(9x+6)−(x+9)<−4(−4x+9)−4(−3)+5(9x+6)
- Solve for xxx. 3(6−7x)−7(8x−3)>3(x+1)3(6-7x)-7(8x-3)>3(x+1)3(6−7x)−7(8x−3)>3(x+1)
- Cooper wants to drive to a writing conference. He needs to rent a car to do so and there's two companies. Company 1 charges him 30\3030 flat rate and 0.08\0.080.08 for each addi…
- Solve for xxx: 17x−68+3x>9217x-68+3x > 9217x−68+3x>92
- Solve the inequality. 12x−6(4x+1)≥−1+3(x−20)12x-6(4x+1)\geq{-1+3(x-20)}12x−6(4x+1)≥−1+3(x−20)
- Solve the inequality 5−5(4x−3)<10(x−4)5-5(4x-3)<10(x-4)5−5(4x−3)<10(x−4)
- Solve for xxx if 5−4x<3−2x5-4x < 3-2x5−4x<3−2x.
- Solve for xxx: 23x+7=2x−3\frac{2}{3}x + 7 = 2x - 332x+7=2x−3