Solve the inequality. $$ 8 x+6-4 x

Question

Solve the inequality. $$ 8 x+6-4 x<8+2 x+10 $$

UpStudy AI · Accepted Answer

To solve the inequality:

$$
8x + 6 - 4x < 8 + 2x + 10
$$

**Step 1: Simplify Both Sides**

Combine like terms on each side of the inequality.

- **Left Side:**
  $$
  8x - 4x + 6 = 4x + 6
  $$

- **Right Side:**
  $$
  8 + 10 + 2x = 18 + 2x
  $$

So, the inequality becomes:
$$
4x + 6 < 18 + 2x
$$

**Step 2: Isolate the Variable**

Subtract $$2x$$ from both sides to get all terms containing $$x$$ on one side:

$$
4x - 2x + 6 < 18
$$
$$
2x + 6 < 18
$$

Next, subtract 6 from both sides to isolate the term with $$x$$:

$$
2x < 12
$$

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

Divide both sides by 2:

$$
x < 6
$$

**Conclusion:**

The solution to the inequality is:
$$
x < 6
$$

This means that all real numbers less than 6 satisfy the original inequality.
The solution to the inequality is $$ x < 6 $$.

Solve the inequality. \[ 8 x+6-4 x<8+2 x+10 \]