Solve the following equation for $$ x $$ : $$ -4(x-5)+1=-1+3(x+6) $$

Question

UpStudy AI · Accepted Answer

To solve the equation for $$ x $$:

$$
-4(x - 5) + 1 = -1 + 3(x + 6)
$$

**Step 1: Expand both sides**

First, distribute the terms inside the parentheses.

$$
-4(x - 5) + 1 = -4x + 20 + 1 = -4x + 21
$$

$$
-1 + 3(x + 6) = -1 + 3x + 18 = 3x + 17
$$

Now the equation looks like:

$$
-4x + 21 = 3x + 17
$$

**Step 2: Gather like terms**

Subtract $$ 3x $$ from both sides to get all $$ x $$-terms on one side:

$$
-4x - 3x + 21 = 17
$$

$$
-7x + 21 = 17
$$

Next, subtract 21 from both sides to isolate the $$ x $$-term:

$$
-7x = 17 - 21
$$

$$
-7x = -4
$$

**Step 3: Solve for $$ x $$**

Divide both sides by -7:

$$
x = \frac{-4}{-7} = \frac{4}{7}
$$

**Answer:**

$$
x = \frac{4}{7}
$$
$$ x = \frac{4}{7} $$

Solve the following equation for :