$$ -18+x

Question

$$ -18+x<-(4 x-5)+2 $$ $$ (-\infty,-10) $$ $$ (-\infty,-30) $$ No Solution $$ (-\infty, 5) $$

UpStudy AI · Accepted Answer

To solve the inequality $$ -18 + x < - (4x - 5) + 2 $$, we first simplify the right side of the inequality.

1. Distribute the negative sign:
   $$
   - (4x - 5) = -4x + 5
   $$
   So the inequality becomes:
   $$
   -18 + x < -4x + 5 + 2
   $$

2. Combine like terms on the right side:
   $$
   -18 + x < -4x + 7
   $$

3. Now, let's isolate $$ x $$ by adding $$ 4x $$ to both sides:
   $$
   -18 + x + 4x < 7
   $$
   This simplifies to:
   $$
   -18 + 5x < 7
   $$

4. Next, add 18 to both sides:
   $$
   5x < 7 + 18
   $$
   Which simplifies to:
   $$
   5x < 25
   $$

5. Finally, divide both sides by 5:
   $$
   x < 5
   $$

Thus, the solution to the inequality is:
$$
(-\infty, 5)
$$

So the correct answer is $$ (-\infty, 5) $$.
The solution to the inequality is $$ (-\infty, 5) $$.

\( -18+x<-(4 x-5)+2 \) \( (-\infty,-10) \) \( (-\infty,-30) \) No Solution \( (-\infty, 5) \)