1-Variable Equations & Inequalities Online Practice

Answer 1

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

1. Solve for \( x \): \[ 2x + 3 = 11 \]

2. Solve for \( x \): \[ 5 - 3x = 2 \]

3. Solve for \( x \): \[ 4(x + 2) = 28 \]

4. Solve for \( x \): \[ \frac{x}{2} - 5 = 7 \]

5. Solve for \( x \): \[ 3x + 4 = 2x - 6 \]

Inequalities

1. Solve the inequality: \[ 3x - 1 < 5 \]

2. Solve the inequality: \[ -2x + 4 \geq 10 \]

3. Solve the inequality: \[ 5 - x > 2x + 1 \]

4. Solve the inequality: \[ 4x + 7 \leq 3x + 15 \]

5. Solve the inequality: \[ -3(x - 2) > 6 \]

Solutions

Equations:

1. \( 2x + 3 = 11 \)

   • Subtract 3: \( 2x = 8 \)
   • Divide by 2: \( x = 4 \)

2. \( 5 - 3x = 2 \)

   • Subtract 5: \( -3x = -3 \)
   • Divide by -3: \( x = 1 \)

3. \( 4(x + 2) = 28 \)

   • Divide by 4: \( x + 2 = 7 \)
   • Subtract 2: \( x = 5 \)

4. \( \frac{x}{2} - 5 = 7 \)

   • Add 5: \( \frac{x}{2} = 12 \)
   • Multiply by 2: \( x = 24 \)

5. \( 3x + 4 = 2x - 6 \)

   • Subtract \( 2x \): \( x + 4 = -6 \)
   • Subtract 4: \( x = -10 \)

Inequalities:

1. \( 3x - 1 < 5 \)

   • Add 1: \( 3x < 6 \)
   • Divide by 3: \( x < 2 \)

2. \( -2x + 4 \geq 10 \)

   • Subtract 4: \( -2x \geq 6 \)
   • Divide by -2 (flip the inequality): \( x \leq -3 \)

3. \( 5 - x > 2x + 1 \)

   • Add \( x \): \( 5 > 3x + 1 \)
   • Subtract 1: \( 4 > 3x \)
   • Divide by 3: \( \frac{4}{3} > x \) or \( x < \frac{4}{3} \)

4. \( 4x + 7 \leq 3x + 15 \)

   • Subtract \( 3x \): \( x + 7 \leq 15 \)
   • Subtract 7: \( x \leq 8 \)

5. \( -3(x - 2) > 6 \)

   • 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!