Solve Inequalities with Addition or Subtraction — Examples
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- Subtracting Like you may have seen before in using addition to solve inequalities, you can simplify inequalities by subtracting. It's very similar to simplifying equations. We w…
By Andrew Wang, Zora Gilbert, Alex Federspiel, Jonathan Heller, Caroline K, Joshua Siktar
- (Video) Solving Basic Linear Inequalities by PatrickJMT Patrick JMT goes through some basic inequalities using subtraction. Summary\large{\text{Summary}}Summary When dealing wit…
By Ben Ferrara, Alex Federspiel, Joshua Siktar, Amy Feraco, Jonathan Heller, Caroline K
- Solving Inequalities by Adding Inequalities are very much like equations. If you want to add or subtract from one side of the equation, you must perform the same operation to th…
By Eunji Kwon, Amy Feraco, Jonathan Heller, Alex Federspiel, Caroline K, Joshua Siktar
- Solving Inequalities by Subtracting Inequalities act very similarly to equations. If you want to add or subtract from one side of the equation, you must perform the same operati…
By Eunji Kwon, Alex Federspiel, Caroline K, Joshua Siktar
- Using Addition to Solve Inequalities When we use addition to solve an inequality, it's the same as using addition to solve a regular equation! Just remember to add the same valu…
By Caroline K, Alex Federspiel, Joshua Siktar
Problems 59
- What is the largest value of xxx such that x+4≤2x+4\leq2x+4≤2?
- The inequality x−5>10x - 5 > 10x−5>10 can be simplified as which of the following?
- If x+1.2≥2x+1.2 \ge 2x+1.2≥2, what is the smallest possible value of xxx, as a decimal?
- If 2.2≥x+1.12.2 \ge x+1.12.2≥x+1.1, what is the largest possible value of xxx, as a decimal?
- The inequality 2x+4<242x+4<242x+4<24 can be simplified to which of the following?
- Solve for xxx: x−7>7x-7>7x−7>7
- Write the solution for the following inequality: x+12≤29x+12\leq29x+12≤29
- Solve for xxx: x+7>10x+7 > 10x+7>10
- Solve for xxx. x+4−(1+8)>18x+4-(1+8)>18x+4−(1+8)>18
- 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. x+9>18−(−4)x+9>18-(-4)x+9>18−(−4)
- Suppose xxx and yyy are real numbers such that x+1<y+2x+1<y+2x+1<y+2 and y+2<14y+2<14y+2<14. What numbers is xxx less than for sure?
- Solve the inequality. x+6>7x + 6 > 7x+6>7
- The additive property of inequality states that: For all real numbers aaa, bbb, and ccc, a>ba>ba>b if and only if a+c>b+c‾\underline{\phantom{a+c>b+c}}a+c>b+c.
- Which of the following inequalities is represented by the number line above?
- Which of the following represents a possible first step in simplifying the equation 3x−2≥−2x+13x-2\geq{-2x+1}3x−2≥−2x+1, with xxx isolated on one side?
- Which of the following correctly shows the additive property of inequality for the inequality 5x<105x<105x<10?
- You and your friend rode the seesaw in middle school. Five years later, you both gained 10 pounds and rode the same seesaw. What changed about your balance?
- Consider the inequality 7x>5x7x>5x7x>5x. What is the smallest number you could fill in the blank while guaranteeing the following inequality to be true? 7x+3+ 77‾ >5x+107x+3+\,\…
- Solve the inequality x−(7+3)+4>6+(7−3)−8x-(7+3)+4>6+(7-3)-8x−(7+3)+4>6+(7−3)−8 for xxx.
- Which of the following represents the inequality x−6≥−3−1−3x-6\geq{-3-1-3}x−6≥−3−1−3
- Solve x+97+(17+27)<67x+\frac{9}{7}+\left(\frac{1}{7}+\frac{2}{7}\right)<\frac{6}{7}x+79+(71+72)<76
- The subtraction property for inequalities says that if equal‾\underline{\phantom{equal}}equal values are subtracted from both sides of an inequality, then the result is an ineq…
- Which of the following is not a correct representation of the subtraction property for inequalities?
- Solve for xxx. x+3>7x+3>7x+3>7
- Solve x+(1.5⋅7)≤9x+\left(1.5\cdot7\right)\leq{9}x+(1.5⋅7)≤9
- Which of the following inequalities does the number line above represent?
- Which of the following lines above represents the inequality −3+x−7>37+8-3+x-7>37+8−3+x−7>37+8?
- Solve (7+2−1)−11−5+x≤(7⋅2)+5(7+2-1)-11-5+x\leq{(7\cdot{2})+5}(7+2−1)−11−5+x≤(7⋅2)+5 for xxx.
- What can we do to get xxx by itself in x−7≤3+2−8x-7\leq{3+2-8}x−7≤3+2−8?
- If x+12−3≤23x+12-3 \leq 23x+12−3≤23 which numbers are xxx less than for sure?
- If 4+x<5+64 +x < 5+64+x<5+6, what numbers could xxx be greater than?
- If x<y−213x < y - \frac{21}{3}x<y−321, solve for yyy in terms of xxx.
- Solve.x−2<39x-2<39x−2<39
- Solve.x+5>38x+5>38x+5>38
- Solve.x−91<59x-91<59x−91<59
- Solve.x+51>−65x+51>-65x+51>−65
- Solve.x−69<24x-69<24x−69<24
- Solve.x+23>−56x+23>-56x+23>−56
- Solve.x−9<22x-9<22x−9<22
- Solve.x+45>46x+45>46x+45>46
- Solve.x−83<−54x-83<-54x−83<−54
- Solve.x+80>59x+80>59x+80>59
- Solve. x+72<−63−3x+72<-63-3x+72<−63−3
- Solve. x−5>30−61x-5>30-61x−5>30−61
- 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. 8x<200−2x8x<200-2x8x<200−2x
- Solve 0≥1−x0\geq 1-x0≥1−x for xxx.
- Simplify the following inequality: −13x<−16x−12-\frac{1}{3}x<-\frac{1}{6}x-12−31x<−61x−12
- Solve. 4−x≥84-x\ge84−x≥8
- Solve. x−8≤−3x-8\le-3x−8≤−3
- Simplify. x+9≥4x + 9 \geq 4x+9≥4
- What is the smallest value of xxx that satisfies the following inequality? x+3≥18x+3 \geq 18x+3≥18
- Simplify the following inequality. x+19≤−19x+19 \leq -19x+19≤−19
- Which of the following inequalities are equivalent to 8x+9≥1?8x+9 \geq 1?8x+9≥1?
- Solve the inequality x+12≥3x+4x + 12 \geq 3x + 4x+12≥3x+4.