equations. Show work! 1. $$ 2 x+5=13 $$ 2. $$ 3 x-4=11 $$ 11. $$ 4 x-6=18 $$ 3. $$ 4 x+7=23 $$ 12. $$ 0.25 x+5=\varepsilon $$ 4. $$ 5 x-3=17 $$ 5. $$ 3 x+2=11 $$ 6. $$ 7 x-9=20 $$ 7. $$ \frac{1}{2} x+6=10 $$ 8. $$ 2 x-5=13 $$ 9. $$ 0.5 x+4=9 $$ 10. $$ 3 x+1=10 $$

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1. Solve $$ 2x+5=13 $$:
   - Subtract 5 from both sides: 
     $$
     2x=13-5=8
     $$
   - Divide both sides by 2: 
     $$
     x=\frac{8}{2}=4
     $$

2. Solve $$ 3x-4=11 $$:
   - Add 4 to both sides: 
     $$
     3x=11+4=15
     $$
   - Divide both sides by 3: 
     $$
     x=\frac{15}{3}=5
     $$

11. Solve $$ 4x-6=18 $$:
   - Add 6 to both sides: 
     $$
     4x=18+6=24
     $$
   - Divide both sides by 4: 
     $$
     x=\frac{24}{4}=6
     $$

3. Solve $$ 4x+7=23 $$:
   - Subtract 7 from both sides: 
     $$
     4x=23-7=16
     $$
   - Divide by 4: 
     $$
     x=\frac{16}{4}=4
     $$

12. Solve $$ 0.25x+5=\varepsilon $$:
   - Subtract 5 from both sides: 
     $$
     0.25x=\varepsilon-5
     $$
   - Multiply both sides by 4 (since $$0.25=\frac{1}{4}$$) to solve for $$x$$: 
     $$
     x=4\left(\varepsilon-5\right)=4\varepsilon-20
     $$

4. Solve $$ 5x-3=17 $$:
   - Add 3 to both sides: 
     $$
     5x=17+3=20
     $$
   - Divide by 5: 
     $$
     x=\frac{20}{5}=4
     $$

5. Solve $$ 3x+2=11 $$:
   - Subtract 2 from both sides: 
     $$
     3x=11-2=9
     $$
   - Divide by 3: 
     $$
     x=\frac{9}{3}=3
     $$

6. Solve $$ 7x-9=20 $$:
   - Add 9 to both sides: 
     $$
     7x=20+9=29
     $$
   - Divide by 7: 
     $$
     x=\frac{29}{7}
     $$

7. Solve $$ \frac{1}{2}x+6=10 $$:
   - Subtract 6 from both sides: 
     $$
     \frac{1}{2}x=10-6=4
     $$
   - Multiply by 2: 
     $$
     x=4\times2=8
     $$

8. Solve $$ 2x-5=13 $$:
   - Add 5 to both sides: 
     $$
     2x=13+5=18
     $$
   - Divide by 2: 
     $$
     x=\frac{18}{2}=9
     $$

9. Solve $$ 0.5x+4=9 $$:
   - Subtract 4 from both sides: 
     $$
     0.5x=9-4=5
     $$
   - Multiply by 2 (since $$0.5=\frac{1}{2}$$): 
     $$
     x=5\times2=10
     $$

10. Solve $$ 3x+1=10 $$:
    - Subtract 1 from both sides: 
      $$
      3x=10-1=9
      $$
    - Divide by 3: 
      $$
      x=\frac{9}{3}=3
      $$
Here are the solutions to the equations: 1. $$ x = 4 $$ 2. $$ x = 5 $$ 11. $$ x = 6 $$ 3. $$ x = 4 $$ 12. $$ x = 4\varepsilon - 20 $$ 4. $$ x = 4 $$ 5. $$ x = 3 $$ 6. $$ x = \frac{29}{7} $$ 7. $$ x = 8 $$ 8. $$ x = 9 $$ 9. $$ x = 10 $$ 10. $$ x = 3 $$

equations. Show work! 1. \( 2 x+5=13 \) 2. \( 3 x-4=11 \) 11. \( 4 x-6=18 \) 3. \( 4 x+7=23 \) 12. \( 0.25 x+5=\varepsilon \) 4. \( 5 x-3=17 \) 5. \( 3 x+2=11 \) 6. \( 7 x-9=20 \) 7. \( \frac{1}{2} x+6=10 \) 8. \( 2 x-5=13 \) 9. \( 0.5 x+4=9 \) 10. \( 3 x+1=10 \)

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