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Summary. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number. Swapping left and right hand sides.
Sep 13, 2023 · Example: 3x + 8 < 26. Again, to solve the inequality you have to isolate the variable x by performing inverse operations as follows: 3x + 8 < 26. 3x - 8 < 26 - 8. 3x < 18. 3x/3 < 18/3. x < 6. Solving this example required two steps (step one: subtract 8 from both sides; step two: divide both sides by 3).
All but one of the techniques learned for solving linear equations apply to solving linear inequalities. You may add or subtract any real number to both sides of an inequality, and you may multiply or divide both sides by any positive real number to create equivalent inequalities. For example: 10> − 5. 10− 7> − 5− 7 Subtract7onbothsides.
Sep 27, 2020 · Start the solution process as before, and at the end, you can move the variable to the left to write the final solution. Divide both sides by − 12 to isolate the variable. Since you are dividing by a negative number, you need to change the direction of the inequality sign. − 1 2> − 12x − 1 2 − 12> − 12x − 12.
- To solve this inequality, we want to find all values of [latex]x[/latex] that can satisfy it.
- This example illustrates what happens to the inequality symbol when divided by a negative number.
- In this problem, I have variables on both sides of the inequality. Although it doesn’t matter where we keep the variable, left or right, it makes sense to be consistent all the time by isolating it on the left side.
- I constructed this problem to emphasize the step required in dealing with the parenthesis symbol.
To solve one-variable linear inequalities, such as x ≥ −3, follow these steps: Multiply through to clear any denominators. Use addition and subtraction to get all the variable-containing terms on one side of the inequality symbol, and all the loose numbers on the other side of the inequality symbol. Simplify on each side of the inequality ...
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Feb 13, 2022 · Exercise 2.7.25. Solve the inequality 8p + 3(p − 12)> 7p − 28 graph the solution on the number line, and write the solution in interval notation. Subtract 7p from both sides to collect the variables on the left. Add 36 to both sides to collect the constants on the right.
