Summers Cross
09/19/2024 · High School
Express the set \( -2 x-8<2 x+8 \) using interval notation. To enter the infinity symbol, \( \infty \), use two lowercase o's: oo Submit Question
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Step-by-step Solution
Solve the equation \( -2x-8<2x+8 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(-2x-8<2x+8\)
- step1: Move the variable to the left side:
\(-2x-8-2x<8\)
- step2: Subtract the terms:
\(-4x-8<8\)
- step3: Move the constant to the right side:
\(-4x<8+8\)
- step4: Add the numbers:
\(-4x<16\)
- step5: Change the signs:
\(4x>-16\)
- step6: Divide both sides:
\(\frac{4x}{4}>\frac{-16}{4}\)
- step7: Divide the numbers:
\(x>-4\)
The solution to the inequality \( -2x-8<2x+8 \) is \( x > -4 \).
To express this solution in interval notation, we can write it as \( (-4, \infty) \).
Quick Answer
\( (-4, \infty) \)
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