All Work Must be shown! 1. $$ -6 y=0 $$ $$ -13-7=0 \quad y=13 x-13) $$ $$ -13-x=0 \quad x=13 x(-13) $$ 3) $$ 2 x+\frac{2 x}{2-5}+\frac{10}{2} $$ 5) $$ 4 x-9-17 $$ 6.) $$ 3 x+5=29 $$ 7) $$ 2 x-5=-21 $$ 8) $$ -10+2 x+5 x+65 $$ $$ 9)=7=-6 x+4 x+5 $$ 10.) $$ 1 x-38+2 x+9 $$ 11) $$ 9 \cdot 5 x-4 x-90 $$ 12) $$ 6=x \cdot 4 x+6 $$

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UpStudy AI · Accepted Answer

Certainly! I'll provide step-by-step solutions for each of the equations you've listed. Some of the equations appear to have formatting issues or may be incomplete. I'll address each one based on the information provided.

---

### **Problem 1**
$$
-6y = 0
$$

**Solution:**

To solve for $$ y $$, divide both sides of the equation by $$-6$$:

$$
\frac{-6y}{-6} = \frac{0}{-6} \
y = 0
$$

**Answer:** $$ y = 0 $$

---

### **Problem 2**
$$
y = 13x - 13
$$

**Solution:**

The equation is already solved for $$ y $$. However, if you're looking to solve for $$ x $$, you can rearrange the equation:

$$
y = 13x - 13 \
y + 13 = 13x \
x = \frac{y + 13}{13}
$$

If there's additional information or another equation related to this, please provide it for a more comprehensive solution.

---

### **Problem 3**
$$
-13 - x = 0
$$

**Solution:**

To solve for $$ x $$, add $$ x $$ to both sides and add 13 to both sides:

$$
-13 - x + x = 0 + x \
-13 = x \
x = -13
$$

**Answer:** $$ x = -13 $$

---

### **Problem 5**
$$
2x + \frac{2x}{2 - 5} + \frac{10}{2} = 0
$$

**Solution:**

First, simplify the denominators and fractions:

$$
2x + \frac{2x}{-3} + 5 = 0
$$

To eliminate the fraction, multiply every term by $$-3$$:

$$
-3(2x) + (-3)\left(\frac{2x}{-3}\right) + (-3)(5) = -3(0) \
-6x + 2x - 15 = 0 \
-4x - 15 = 0
$$

Now, solve for $$ x $$:

$$
-4x = 15 \
x = \frac{15}{-4} \
x = -\frac{15}{4}
$$

**Answer:** $$ x = -\dfrac{15}{4} $$

---

### **Problem 6**
$$
3x + 5 = 29
$$

**Solution:**

Subtract 5 from both sides:

$$
3x = 29 - 5 \
3x = 24
$$

Now, divide by 3:

$$
x = \frac{24}{3} \
x = 8
$$

**Answer:** $$ x = 8 $$

---

### **Problem 7**
$$
2x - 5 = -21
$$

**Solution:**

Add 5 to both sides:

$$
2x = -21 + 5 \
2x = -16
$$

Now, divide by 2:

$$
x = \frac{-16}{2} \
x = -8
$$

**Answer:** $$ x = -8 $$

---

### **Problem 8**
$$
-10 + 2x + 5x + 65 = 0
$$

**Solution:**

Combine like terms:

$$
(-10 + 65) + (2x + 5x) = 0 \
55 + 7x = 0
$$

Now, solve for $$ x $$:

$$
7x = -55 \
x = \frac{-55}{7}
$$

**Answer:** $$ x = -\dfrac{55}{7} $$

---

### **Problem 9**
$$
7 = -6x + 4x + 5
$$

**Solution:**

Combine like terms on the right side:

$$
7 = (-6x + 4x) + 5 \
7 = -2x + 5
$$

Subtract 5 from both sides:

$$
7 - 5 = -2x \
2 = -2x
$$

Now, divide by $$-2$$:

$$
x = \frac{2}{-2} \
x = -1
$$

**Answer:** $$ x = -1 $$

---

### **Problem 10**
$$
x - 38 + 2x + 9 = 0
$$

**Solution:**

Combine like terms:

$$
(x + 2x) + (-38 + 9) = 0 \
3x - 29 = 0
$$

Now, solve for $$ x $$:

$$
3x = 29 \
x = \frac{29}{3}
$$

**Answer:** $$ x = \dfrac{29}{3} $$

---

### **Problem 11**
$$
9 \cdot 5x - 4x - 90 = 0
$$

**Solution:**

First, perform the multiplication:

$$
45x - 4x - 90 = 0
$$

Combine like terms:

$$
(45x - 4x) - 90 = 0 \
41x - 90 = 0
$$

Now, solve for $$ x $$:

$$
41x = 90 \
x = \frac{90}{41}
$$

**Answer:** $$ x = \dfrac{90}{41} $$

---

### **Problem 12**
$$
6 = x \cdot 4x + 6
$$
$$
\text{or} \quad 6 = 4x^2 + 6
$$

**Solution:**

Assuming the equation is:

$$
6 = 4x^2 + 6
$$

Subtract 6 from both sides:

$$
0 = 4x^2
$$

Divide by 4:

$$
x^2 = 0 \
x = 0
$$

**Alternative Interpretation:**

If the equation is:

$$
6 = x(4x) + 6 \
6 = 4x^2 + 6
$$

The solution remains the same as above.

**Answer:** $$ x = 0 $$

---

**Note:** If there's any additional information or if some equations were meant to be different, please provide the corrected versions, and I'd be happy to help further!
Here are the solutions to the equations: 1. $$ y = 0 $$ 2. $$ x = -13 $$ 3. $$ x = -\dfrac{15}{4} $$ 4. $$ x = 8 $$ 5. $$ x = -8 $$ 6. $$ x = -\dfrac{55}{7} $$ 7. $$ x = -1 $$ 8. $$ x = \dfrac{29}{3} $$ 9. $$ x = \dfrac{90}{41} $$ 10. $$ x = 0 $$ If there are more equations or additional information, please let me know!

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