It sounds like you're looking for practice on 1-variable equations and inequalities. Here are some examples, along with solutions to help you learn. You can try solving these on your own first, then check the solutions!
Equations
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Solve for \( x \): \[ 2x + 3 = 11 \]
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Solve for \( x \): \[ 5 - 3x = 2 \]
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Solve for \( x \): \[ 4(x + 2) = 28 \]
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Solve for \( x \): \[ \frac{x}{2} - 5 = 7 \]
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Solve for \( x \): \[ 3x + 4 = 2x - 6 \]
Inequalities
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Solve the inequality: \[ 3x - 1 < 5 \]
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Solve the inequality: \[ -2x + 4 \geq 10 \]
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Solve the inequality: \[ 5 - x > 2x + 1 \]
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Solve the inequality: \[ 4x + 7 \leq 3x + 15 \]
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Solve the inequality: \[ -3(x - 2) > 6 \]
Solutions
Equations:
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\( 2x + 3 = 11 \)
- Subtract 3: \( 2x = 8 \)
- Divide by 2: \( x = 4 \)
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\( 5 - 3x = 2 \)
- Subtract 5: \( -3x = -3 \)
- Divide by -3: \( x = 1 \)
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\( 4(x + 2) = 28 \)
- Divide by 4: \( x + 2 = 7 \)
- Subtract 2: \( x = 5 \)
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\( \frac{x}{2} - 5 = 7 \)
- Add 5: \( \frac{x}{2} = 12 \)
- Multiply by 2: \( x = 24 \)
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\( 3x + 4 = 2x - 6 \)
- Subtract \( 2x \): \( x + 4 = -6 \)
- Subtract 4: \( x = -10 \)
Inequalities:
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\( 3x - 1 < 5 \)
- Add 1: \( 3x < 6 \)
- Divide by 3: \( x < 2 \)
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\( -2x + 4 \geq 10 \)
- Subtract 4: \( -2x \geq 6 \)
- Divide by -2 (flip the inequality): \( x \leq -3 \)
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\( 5 - x > 2x + 1 \)
- Add \( x \): \( 5 > 3x + 1 \)
- Subtract 1: \( 4 > 3x \)
- Divide by 3: \( \frac{4}{3} > x \) or \( x < \frac{4}{3} \)
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\( 4x + 7 \leq 3x + 15 \)
- Subtract \( 3x \): \( x + 7 \leq 15 \)
- Subtract 7: \( x \leq 8 \)
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\( -3(x - 2) > 6 \)
- Distribute: \( -3x + 6 > 6 \)
- Subtract 6: \( -3x > 0 \)
- Divide by -3 (flip the inequality): \( x < 0 \)
Feel free to reach out if you need more practice problems or further explanations!