Let's solve each of these two-step equations step-by-step.
1. [tex]\( 5X + 4 = 19 \)[/tex]
- Subtract 4 from both sides: [tex]\( 5X = 15 \)[/tex]
- Divide both sides by 5: [tex]\( X = 3.0 \)[/tex]
2. [tex]\( \frac{x}{2} - 8 = -1 \)[/tex]
- Add 8 to both sides: [tex]\( \frac{x}{2} = 7 \)[/tex]
- Multiply both sides by 2: [tex]\( X = 14 \)[/tex]
3. [tex]\( 7X - 4 = 10 \)[/tex]
- Add 4 to both sides: [tex]\( 7X = 14 \)[/tex]
- Divide both sides by 7: [tex]\( X = 2.0 \)[/tex]
4. [tex]\( \frac{x}{2} - 8 = -4 \)[/tex]
- Add 8 to both sides: [tex]\( \frac{x}{2} = 4 \)[/tex]
- Multiply both sides by 2: [tex]\( X = 8 \)[/tex]
5. [tex]\( 16 - 4X = 0 \)[/tex]
- Subtract 16 from both sides: [tex]\( -4X = -16 \)[/tex]
- Divide both sides by -4: [tex]\( X = 4.0 \)[/tex]
6. [tex]\( \frac{x}{-2} - 5 = -2 \)[/tex]
- Add 5 to both sides: [tex]\( \frac{x}{-2} = 3 \)[/tex]
- Multiply both sides by -2: [tex]\( X = -6 \)[/tex]
7. [tex]\( \frac{x}{5} - 2 = 1 \)[/tex]
- Add 2 to both sides: [tex]\( \frac{x}{5} = 3 \)[/tex]
- Multiply both sides by 5: [tex]\( X = 15 \)[/tex]
8. [tex]\( 2X - 12 = 8 \)[/tex]
- Add 12 to both sides: [tex]\( 2X = 20 \)[/tex]
- Divide both sides by 2: [tex]\( X = 10.0 \)[/tex]
9. [tex]\( \frac{x}{2} - 7 = 2 \)[/tex]
- Add 7 to both sides: [tex]\( \frac{x}{2} = 9 \)[/tex]
- Multiply both sides by 2: [tex]\( X = 18 \)[/tex]
10. [tex]\( -2 = 6 + 8X \)[/tex]
- Subtract 6 from both sides: [tex]\( -8 = 8X \)[/tex]
- Divide both sides by 8: [tex]\( X = -1.0 \)[/tex]
11. [tex]\( 3 - 2X = 9 \)[/tex]
- Subtract 3 from both sides: [tex]\( -2X = 6 \)[/tex]
- Divide both sides by -2: [tex]\( X = 3.0 \)[/tex]
So, the solutions to the equations are:
1. [tex]\( X = 3.0 \)[/tex]
2. [tex]\( X = 14 \)[/tex]
3. [tex]\( X = 2.0 \)[/tex]
4. [tex]\( X = 8 \)[/tex]
5. [tex]\( X = 4.0 \)[/tex]
6. [tex]\( X = -6 \)[/tex]
7. [tex]\( X = 15 \)[/tex]
8. [tex]\( X = 10.0 \)[/tex]
9. [tex]\( X = 18 \)[/tex]
10. [tex]\( X = -1.0 \)[/tex]
11. [tex]\( X = 3.0 \)[/tex]
