Solve $$ 5 x-10+3=-7 x+28 $$ for $$ x $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 5x - 10 + 3 = -7x + 28 $$ for $$ x $$, follow these steps:

1. **Simplify Both Sides of the Equation**

Start by simplifying the left side (LS) of the equation:

$$
   5x - 10 + 3 = 5x - 7
   $$

So, the equation becomes:

$$
   5x - 7 = -7x + 28
   $$

2. **Move Variable Terms to One Side**

To collect like terms, add $$ 7x $$ to both sides to move all $$ x $$-terms to the left side:

$$
   5x + 7x - 7 = 28
   $$
   
   $$
   12x - 7 = 28
   $$

3. **Move Constant Terms to the Other Side**

Next, add $$ 7 $$ to both sides to isolate the term with $$ x $$:

$$
   12x = 28 + 7
   $$
   
   $$
   12x = 35
   $$

4. **Solve for $$ x $$**

Finally, divide both sides by $$ 12 $$ to solve for $$ x $$:

$$
   x = \frac{35}{12}
   $$
   
   $$
   x = 2 \frac{11}{12}
   $$

**Final Answer:**
$$
x = \frac{35}{12} \quad \text{or} \quad x = 2 \frac{11}{12}
$$
$$ x = \frac{35}{12} $$ or $$ x = 2 \frac{11}{12} $$

Solve \( 5 x-10+3=-7 x+28 \) for \( x \)