$$ \begin{array}{r} ext { Solve the following two-step } \ ext { equations. Show work! }\end{array} $$ $$ \begin{array}{l}1.2 x+5=13 \ ext { 2. } 3 x-4=11 \quad 11.4 x-6=18 \ ext { 3. } 4 x+7=23 \ ext { 4. } 5 x-3=17 \ ext { 5. } 3 x+2=11 \ ext { 6. } 7 x-9=20 \ ext { 7. } \frac{1}{2} x+6=10 \ ext { 8. } 2 x-5=13 \ ext { 9. } 0 \cdot 5 x+4=9 \ ext { 10. } 3 x+1=10\end{array} $$

Question

$$ \begin{array}{r}	ext { Solve the following two-step } \ 	ext { equations. Show work! }\end{array} $$ $$ \begin{array}{l}1.2 x+5=13 \ 	ext { 2. } 3 x-4=11 \quad 11.4 x-6=18 \ 	ext { 3. } 4 x+7=23 \ 	ext { 4. } 5 x-3=17 \ 	ext { 5. } 3 x+2=11 \ 	ext { 6. } 7 x-9=20 \ 	ext { 7. } \frac{1}{2} x+6=10 \ 	ext { 8. } 2 x-5=13 \ 	ext { 9. } 0 \cdot 5 x+4=9 \ 	ext { 10. } 3 x+1=10\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3x+1=10$$
- step1: Move the constant to the right side:
  $$3x=10-1$$
- step2: Subtract the numbers:
  $$3x=9$$
- step3: Divide both sides:
  $$\frac{3x}{3}=\frac{9}{3}$$
- step4: Divide the numbers:
  $$x=3$$
Solve the equation $$ 5x-3=17 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$5x-3=17$$
- step1: Move the constant to the right side:
  $$5x=17+3$$
- step2: Add the numbers:
  $$5x=20$$
- step3: Divide both sides:
  $$\frac{5x}{5}=\frac{20}{5}$$
- step4: Divide the numbers:
  $$x=4$$
Solve the equation $$ 3x-4=11 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3x-4=11$$
- step1: Move the constant to the right side:
  $$3x=11+4$$
- step2: Add the numbers:
  $$3x=15$$
- step3: Divide both sides:
  $$\frac{3x}{3}=\frac{15}{3}$$
- step4: Divide the numbers:
  $$x=5$$
Solve the equation $$ 1.2x+5=13 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$1.2x+5=13$$
- step1: Move the constant to the right side:
  $$1.2x=13-5$$
- step2: Subtract the numbers:
  $$1.2x=8$$
- step3: Divide both sides:
  $$\frac{1.2x}{1.2}=\frac{8}{1.2}$$
- step4: Divide the numbers:
  $$x=\frac{20}{3}$$
Solve the equation $$ \frac{1}{2}x+6=10 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{1}{2}x+6=10$$
- step1: Move the constant to the right side:
  $$\frac{1}{2}x=10-6$$
- step2: Subtract the numbers:
  $$\frac{1}{2}x=4$$
- step3: Multiply by the reciprocal:
  $$\frac{1}{2}x\times 2=4\times 2$$
- step4: Multiply:
  $$x=8$$
Solve the equation $$ 3x+2=11 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$3x+2=11$$
- step1: Move the constant to the right side:
  $$3x=11-2$$
- step2: Subtract the numbers:
  $$3x=9$$
- step3: Divide both sides:
  $$\frac{3x}{3}=\frac{9}{3}$$
- step4: Divide the numbers:
  $$x=3$$
Solve the equation $$ 7x-9=20 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$7x-9=20$$
- step1: Move the constant to the right side:
  $$7x=20+9$$
- step2: Add the numbers:
  $$7x=29$$
- step3: Divide both sides:
  $$\frac{7x}{7}=\frac{29}{7}$$
- step4: Divide the numbers:
  $$x=\frac{29}{7}$$
Solve the equation $$ 4x+7=23 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$4x+7=23$$
- step1: Move the constant to the right side:
  $$4x=23-7$$
- step2: Subtract the numbers:
  $$4x=16$$
- step3: Divide both sides:
  $$\frac{4x}{4}=\frac{16}{4}$$
- step4: Divide the numbers:
  $$x=4$$
Solve the equation $$ 11.4x-6=18 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$11.4x-6=18$$
- step1: Move the constant to the right side:
  $$11.4x=18+6$$
- step2: Add the numbers:
  $$11.4x=24$$
- step3: Divide both sides:
  $$\frac{11.4x}{11.4}=\frac{24}{11.4}$$
- step4: Divide the numbers:
  $$x=\frac{40}{19}$$
Solve the equation $$ 2x-5=13 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$2x-5=13$$
- step1: Move the constant to the right side:
  $$2x=13+5$$
- step2: Add the numbers:
  $$2x=18$$
- step3: Divide both sides:
  $$\frac{2x}{2}=\frac{18}{2}$$
- step4: Divide the numbers:
  $$x=9$$
Solve the equation $$ 0\cdot 5x+4=9 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$0\times 5x+4=9$$
- step1: Simplify:
  $$4=9$$
- step2: The statement is false:
  $$x \in \varnothing $$
Here are the solutions to the equations step by step:

1. **Equation:** $$ 1.2x + 5 = 13 $$

**Step 1:** Subtract 5 from both sides:
   $$
   1.2x = 13 - 5 \implies 1.2x = 8
   $$

**Step 2:** Divide both sides by 1.2:
   $$
   x = \frac{8}{1.2} = \frac{20}{3} \approx 6.67
   $$

2. **Equation:** $$ 3x - 4 = 11 $$

**Step 1:** Add 4 to both sides:
   $$
   3x = 11 + 4 \implies 3x = 15
   $$

**Step 2:** Divide both sides by 3:
   $$
   x = \frac{15}{3} = 5
   $$

3. **Equation:** $$ 11.4x - 6 = 18 $$

**Step 1:** Add 6 to both sides:
   $$
   11.4x = 18 + 6 \implies 11.4x = 24
   $$

**Step 2:** Divide both sides by 11.4:
   $$
   x = \frac{24}{11.4} = \frac{40}{19} \approx 2.11
   $$

4. **Equation:** $$ 4x + 7 = 23 $$

**Step 1:** Subtract 7 from both sides:
   $$
   4x = 23 - 7 \implies 4x = 16
   $$

**Step 2:** Divide both sides by 4:
   $$
   x = \frac{16}{4} = 4
   $$

5. **Equation:** $$ 5x - 3 = 17 $$

**Step 1:** Add 3 to both sides:
   $$
   5x = 17 + 3 \implies 5x = 20
   $$

**Step 2:** Divide both sides by 5:
   $$
   x = \frac{20}{5} = 4
   $$

6. **Equation:** $$ 3x + 2 = 11 $$

**Step 1:** Subtract 2 from both sides:
   $$
   3x = 11 - 2 \implies 3x = 9
   $$

**Step 2:** Divide both sides by 3:
   $$
   x = \frac{9}{3} = 3
   $$

7. **Equation:** $$ 7x - 9 = 20 $$

**Step 1:** Add 9 to both sides:
   $$
   7x = 20 + 9 \implies 7x = 29
   $$

**Step 2:** Divide both sides by 7:
   $$
   x = \frac{29}{7} \approx 4.14
   $$

8. **Equation:** $$ \frac{1}{2}x + 6 = 10 $$

**Step 1:** Subtract 6 from both sides:
   $$
   \frac{1}{2}x = 10 - 6 \implies \frac{1}{2}x = 4
   $$

**Step 2:** Multiply both sides by 2:
   $$
   x = 4 \times 2 = 8
   $$

9. **Equation:** $$ 2x - 5 = 13 $$

**Step 1:** Add 5 to both sides:
   $$
   2x = 13 + 5 \implies 2x = 18
   $$

**Step 2:** Divide both sides by 2:
   $$
   x = \frac{18}{2} = 9
   $$

10. **Equation:** $$ 0 \cdot 5x + 4 = 9 $$

This simplifies to $$ 4 = 9 $$, which is a contradiction. Thus, there is no solution:
   $$
   x \in \varnothing
   $$

11. **Equation:** $$ 3x + 1 = 10 $$

**Step 1:** Subtract 1 from both sides:
   $$
   3x = 10 - 1 \implies 3x = 9
   $$

**Step 2:** Divide both sides by 3:
   $$
   x = \frac{9}{3} = 3
   $$

### Summary of Solutions:
1. $$ x = \frac{20}{3} \approx 6.67 $$
2. $$ x = 5 $$
3. $$ x = \frac{40}{19} \approx 2.11 $$
4. $$ x = 4 $$
5. $$ x = 4 $$
6. $$ x = 3 $$
7. $$ x = \frac{29}{7} \approx 4.14 $$
8. $$ x = 8 $$
9. $$ x \in \varnothing $$ (no solution)
10. $$ x = 3 $$
Here are the solutions to the equations: 1. $$ x = \frac{20}{3} \approx 6.67 $$ 2. $$ x = 5 $$ 3. $$ x = \frac{40}{19} \approx 2.11 $$ 4. $$ x = 4 $$ 5. $$ x = 4 $$ 6. $$ x = 3 $$ 7. $$ x = \frac{29}{7} \approx 4.14 $$ 8. $$ x = 8 $$ 9. No solution 10. $$ x = 3 $$

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