Equivalent Inequalities - Definition & Examples
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- Equivalent Inequalities Equivalent inequalities are inequalities that communicate the same information. There are a few different ways to produce equivalent inequalities. First,…
By Hannah Bonville, Zora Gilbert, Grace Carey, Alex Federspiel, Jonathan Heller, Caroline K
- Equivalent Inequalities If a set of inequalities are equivalent, it means that they all have exactly the same solutions. Say you have a certain inequality and you want to produc…
By Caroline K
- (Video) Equivalent Inequalities by Anusha Rahman In this lesson, Anusha Rahman covers what equivalent inequalities are and how to determine whether inequalities are equivalent. …
By Anusha Rahman
Problems 33
- Solve the inequality 2x−5<92x - 5 < 92x−5<9.
- You are given the inequality x<yx<yx<y. Which inequality below relates the negatives, −x-x−x and −y-y−y, of the two sides?
- 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)))
- Solve for xxx. 2+x11>11\frac{\sqrt{2}+x}{\sqrt{11}}>\sqrt{11}112+x>11
- Which inequalities below are equivalent to 3x+9<6y3x+9<6y3x+9<6y?
- What value of α\alphaα would make the inequality 3x−α≥43x-\alpha \geq 43x−α≥4 equivalent to the inequality 12x−4≥1612x-4 \geq 1612x−4≥16?
- What value of α\alphaα makes the inequality 4x+α<104x+\alpha<104x+α<10 equivalent to the inequality 8x<148x<148x<14?
- Which value of α\alphaα makes the inequality αx−α<6\alpha x - \alpha < 6αx−α<6 equivalent to the inequality x<7x<7x<7?
- Are these inequalities equivalent? 4x+y−3z<18z>4x3+y3+6\begin{gather} 4x+y-3z<18\\ z>\frac{4x}{3}+\frac{y}{3}+6 \end{gather}4x+y−3z<18z>34x+3y+6
- Which inequalities are equivalent? Ineq 1: 2(x−1)<y+4Ineq 2: y>2(x−3)Ineq 3: −x<−(y2+3)\begin{align} &\text{Ineq 1: }\ 2(x-1)<y+4\\ &\text{Ineq 2: }\ y>2(x-3)\\ &\text{Ineq 3: }…
- Let β\betaβ be a real constant. What value of α\alphaα makes the following inequalities equivalent? 2x−α<3y+βx<32(y+β)\begin{gather} 2x-\alpha<3y+\beta\\ x<\frac{3}{2}(y+\beta) …
- Find the smallest integer nnn such that n−n−99<1.\sqrt{n} - \sqrt{n - 99} < 1.n−n−99<1. (Hint: First solve the equation x−x−99=1\sqrt{x} - \sqrt{x - 99} = 1x−x−99=1.)
- Find all real numbers such that x≥0x\ge0x≥0 and x<4x\sqrt x < 4xx<4x.
- Which of the following compound inequalities is equivalent to 2x−3<x+y≤2x+32x-3 < x + y \leq 2x + 32x−3<x+y≤2x+3?
- What do we call numbers that satisfy an inequality?
- Select the operations that would change the direction of the inequality sign.
- Solve the inequality: x2−x−16≥\frac{x}{2}-\frac{x-1}{6}\geq2x−6x−1≥x+210−4\frac{x+2}{10}-410x+2−4
- 73x+5>2+73x\frac{7}{3}x+5>2+\frac{7}{3}x37x+5>2+37x Which of the following inequalities is another correct representation for the inequality above?
- What is the main goal in solving an inequality?
- How could we rewrite the inequality 5x−2≤3+2x5x-2\leq{3+2x}5x−2≤3+2x in an equivalent form?
- Find an equivalent inequality to y>3x+9y > 3x+9y>3x+9 by dividing both sides by 3 and then subtracting 3 from both sides.
- Find an equivalent inequality to 5y>10x+205y > 10x+205y>10x+20 by dividing both sides by 5, subtracting 4 from both sides, and then dividing both sides by 2.
- Suppose you solve the inequality above by the following steps: Subtract the red constant from both sides. Subtract the orange constant from both sides. Divide both sides by the …
- Solve the below inequality for xxx. 3x−7(5−8)+2≤x+2(5−9)3x-7(5-8)+2\leq{x+2(5-9)}3x−7(5−8)+2≤x+2(5−9)
- Simplify the following inequality: −12x−4<−13x-\frac{1}{2}x -4<-\frac{1}{3}x−21x−4<−31x
- Simplify the following inequality: 3(x+3)+5<−x3(x+3)+5 < -x3(x+3)+5<−x
- Solve for xxx: (x+2)2>x2(x+2)^2 > x^2(x+2)2>x2
- For this inequality below, what is the smallest possible value for xxx? −2x+5≤3x-2x+5\leq 3x−2x+5≤3x
- What value of ccc makes the following inequalities equivalent? 3x+2>143x+2 > 143x+2>14 6x+c>146x+c > 146x+c>14
- What value of ccc makes the following inequalities equivalent? 9x−4≤149x-4 \leq 149x−4≤14 11x+c≤2511x+c \leq 2511x+c≤25
- Which of the following inequalities are equivalent to 3x+2≥83x+2 \geq 83x+2≥8?
- What value of ccc makes the following inequalities equivalent? 5x−2<135x-2 < 135x−2<13 7x+c<307x+c < 307x+c<30
- Spider Man is preparing for another day of heroic adventures. He has on his agenda to climb up 161616 different buildings in the city. If xxx is some number greater than 10,10,1…