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Algebra 1
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One-Variable Inequalities
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Solve Compound Inequalities

Solve Compound Inequalities Worksheet

6 problems

Solve compound inequalities
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Solving compound inequalities refers to solving inequalities that have two or more inequalities in them. These inequalities are a combination of two or more inequalities linked by the words “and” or “or”. In this process, we solve for the value of the variable that fits the inequality by using inverse operations but with more than one condition at a time. In these worksheets, students will solve the inequalities linked by “and” or “or”.

For example: Solve `–4>v–17≥–11` for `v`.

Write your answer as a compound inequality with integers.

Choices: `[[13 > v > 6][v > 13 or v ≤ 6][13 > v ≥ 6][v > 13 or v < 6]]`

Algebra 1
One-Variable Inequalities

How Will This Worksheet on "Solve Compound Inequalities" Benefit Your Students' Learning?

  • It enhances problem-solving skills as students need to use different mathematical methods to solve the inequality.
  • It strengthens logical reasoning skills as you learn how different math statements are connected by words like "and" or "or".
  • It improves proficiency of different algebraic concepts such as inequalities, solving equations, and representing solutions visually on a number line.
  • It fosters critical thinking as studen...
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Solved Example

Q. Solve for gg. \newlineg−20>−4g - 20 > -4 or g+19≤3g + 19 \leq 3\newlineWrite your answer as a compound inequality with integers.\newlineChoices:\newline(A) 16≥g≥−1616 \geq g \geq -16\newline(B) g>16g > 16 or g≤−16g \leq -16\newline(C) 16>g≥−1616 > g \geq -16\newline(D) g≥16g \geq 16 or g≤−16g \leq -16
Solution:
  1. Isolate gg in first part: Solve the first part of the compound inequality g−20>−4g - 20 > -4. To isolate gg, we need to add 2020 to both sides of the inequality. \newlineg−20+20>−4+20g - 20 + 20 > -4 + 20 g>16g > 16
  2. Isolate gg in second part: Solve the second part of the compound inequality g+19≤3g + 19 \leq 3. To isolate gg, we need to subtract 1919 from both sides of the inequality. \newlineg+19−19≤3−19g + 19 - 19 \leq 3 - 19 g≤−16g \leq -16
  3. Combine solutions: Combine the solutions from Step 11 and Step 22 to write the final compound inequality.\newlineThe solution is g>16g > 16 or g≤−16g \leq -16.

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