Questions: Solving an "Or" Compound Inequality Graph the solution of this inequality: 2x - 7 > 3, or 4 - x ≤ -4

Solving an "Or" Compound Inequality Graph the solution of this inequality: 2x - 7 > 3, or 4 - x ≤ -4
Transcript text: Solving an "Or" Compound Inequal Graph the solution of this inequality: $2 x-7>3$, or $4-x \leq-4$
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Solution

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Solution Steps

Step 1: Solve the first inequality

The first inequality is \(2x - 7 > 3\).

Add 7 to both sides: \[2x - 7 + 7 > 3 + 7\] \[2x > 10\]

Divide both sides by 2: \[x > 5\]

Step 2: Solve the second inequality

The second inequality is \(4 - x \leq -4\).

Subtract 4 from both sides: \[4 - x - 4 \leq -4 - 4\] \[-x \leq -8\]

Multiply both sides by -1 (and reverse the inequality sign): \[x \geq 8\]

Step 3: Combine the solutions

The solution to the compound inequality \(2x - 7 > 3\) or \(4 - x \leq -4\) is the union of the solutions to the individual inequalities.

From Step 1: \(x > 5\) From Step 2: \(x \geq 8\)

Final Answer

The solution to the compound inequality is \(x > 5\) or \(x \geq 8\). This can be represented on the number line as:

  • An open circle at 5 with an arrow pointing to the right.
  • A closed circle at 8 with an arrow pointing to the right.
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