Solve the inequality $$ 9 x+2

Question

Solve the inequality $$ 9 x+2<8 x-3 $$. Write the solution set in interval notation, and graph it. The solution set is $$ \square $$. (Type your answer in interval notation.)

UpStudy AI · Accepted Answer

Solve the inequality by following steps:
- step0: Solve for $$x$$:
  $$9x+2<8x-3$$
- step1: Move the expression to the left side:
  $$9x-8x<-3-2$$
- step2: Add and subtract:
  $$x<-3-2$$
- step3: Add and subtract:
  $$x<-5$$
To solve the inequality $$ 9x + 2 < 8x - 3 $$, we can follow these steps:

1. **Isolate the variable $$ x $$**:
   - Subtract $$ 8x $$ from both sides:
     $$
     9x - 8x + 2 < -3
     $$
     This simplifies to:
     $$
     x + 2 < -3
     $$

2. **Subtract 2 from both sides**:
   $$
   x < -3 - 2
   $$
   This simplifies to:
   $$
   x < -5
   $$

The solution set in interval notation is:
$$
(-\infty, -5)
$$

### Graphing the Solution
While I cannot provide a graph directly, you can visualize the solution as follows:
- Draw a number line.
- Mark the point $$-5$$ on the line.
- Shade the region to the left of $$-5$$ to indicate that all values less than $$-5$$ are included in the solution set.

Thus, the final answer is:
$$
\text{The solution set is } (-\infty, -5).
$$
The solution set is $$ (-\infty, -5) $$.

Solve the inequality \( 9 x+2<8 x-3 \). Write the solution set in interval notation, and graph it. The solution set is \( \square \). (Type your answer in interval notation.)

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