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Jason Solves It! Inequalities with Multiplication & Division 6Y + 2 < 38 -4x – 8 > 8 that’s me Click for answer x + 4 < -7 3 1
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<ul><li>Just like in an equation, when trying to solve an inequality, you need to isolate the variable. </li></ul><ul><li>It just means you gotta get the variable on a side all by itself. In this inequality, it’s going to take more than one step. </li></ul>An inequality is the relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.” < 38 6Y+2 Y < some number variable Click here for answer Click here for answer
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<ul><li>A variable is a letter or symbol that represents a value… </li></ul><ul><li>Well, to get rid of that 2 on the left side of the inequality, we subtract 2 from both sides. </li></ul>< 38 6Y + 2 The “- 2” on the left side of the inequality cancels out the “+ 2” on the left side. On the right side of the inequality, you just subtract 2 from 38, which is 36. < 38 6Y+2 - 2 - 2 - 2 - 2 < 36 variable Click here to continue Click here for answer
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A linear inequality in one variable is an inequality (1 variable) that can be written in the form ax + b < 0 or ax + b > 0, where a & b are real numbers and a ≠0. Right now, the variable is not isolated, even though there is only one term on the left side. The 6 in front of the Y is our problem. In order to get rid of it, we are going to have to divide both sides of the inequality by 6. 6Y < 36 6 divided by 6 is 1, so those 6’s on the left side cancel each other out. On the right side, 36 divided by 6 is 6. Look at that – we solved the inequality! Y < 6 Click here for answer 6 6 Click here to continue
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If you have a whole number in front of a variable, you will have to divide both sides of the inequality. If the number is a fraction , you will have to multiply both sides of the inequality by the inverse of the fraction. + 8 You are going to start by adding 8 to both sides of the inequality – but that’s pretty much old news now, right? - 8 + 8 = 0, so those eights on the left side of the inequality cancel each other out. On the right side of the inequality, we have 8 + 8, which equals 16. -4x – 8 > 8 + 8 -4x > 16 numbers with a variable Click here for answer Click here to continue There is gonna be an extra step in this one…but you’ll see that when you get there… This inequality looks just like the last one. I just do the same thing, right?
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Like Terms are terms whose variables (and their exponents such as the 2 in x 2 ) are the same. - 4x > 16 x < -4 Just like we usually do, we have to get rid of that -4 in front of the x by dividing both sides by -4, and the -4’s on the left side of the inequality cancel each other out. When you divide both sides of an inequality by a negative number, you have to turn the sign around. Here, > becomes < . Click here to continue Like terms Click here to continue - 4 - 4 Now, it’s time for that extra step, right?
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Remember, when you divide both sides of an inequality by a negative number, you have to switch the sign. Just like we usually do, we are going to get rid of the 4 on the left side of the inequality by subtracting 4 from both sides of the inequality. Then, the 4 and the -4 on the left side cancel each other out. -7 minus 4 is -11, so we are now down to 1/3x = -11. < -7 - 4 - 4 Click here to continue Like terms Click here to continue + 4 1 x 3 Finally, the last inequality! 1 x = -11 3
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Remember, when you divide both sides of an inequality by a negative number, you have to switch the sign. How do we get rid of that 1/3 in front of the x? We are going to have to multiply both sides of the inequality by the reciprocal of the fraction – which is 3. What is 1/3 times 3? 1 of course! So those cancel each other out, x is isolated, and all we have to do is multiply -11 by 3, which is -33, and our inequality is solved! x < -11 (3) (3) x < -33 Click here to continue Like terms Click here to continue 3 1
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<ul><li>Ms. Umberger </li></ul><ul><li>Transition to Algebra </li></ul><ul><li>Don’t panic when you see an inequality you would be amazed how easy they are!! </li></ul>CLASS INFORMATION
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