Solve for $$ d $$ $$ \begin{array}{l}3+d

Question

Solve for $$ d $$ $$ \begin{array}{l}3+d<3-d \ d<6 \ d<-6 \ d<0 \ d<-3\end{array} $$

UpStudy AI · Accepted Answer

To solve for $$ d $$ given the system of inequalities:

$$
\begin{array}{l}
3 + d < 3 - d \
d < 6 \
d < -6 \
d < 0 \
d < -3
\end{array}
$$

Let's analyze each inequality step by step.

---

### 1. Solving $$ 3 + d < 3 - d $$:

$$
\begin{align*}
3 + d &< 3 - d \
\text{Subtract } 3 \text{ from both sides:} \
d &< -d \
\text{Add } d \text{ to both sides:} \
2d &< 0 \
\text{Divide both sides by } 2: \
d &< 0
\end{align*}
$$

**Result:** $$ d < 0 $$

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### 2. Other Inequalities:

- $$ d < 6 $$
- $$ d < -6 $$
- $$ d < 0 $$ (from above)
- $$ d < -3 $$

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### 3. Combining All Inequalities:

To find the solution that satisfies **all** the inequalities simultaneously, identify the most restrictive condition. Here's how they stack up:

- $$ d < 6 $$: Any $$ d $$ less than 6.
- $$ d < -6 $$: More restrictive; $$ d $$ must be less than -6.
- $$ d < 0 $$: Already covered by $$ d < -6 $$.
- $$ d < -3 $$: Also covered by $$ d < -6 $$.

The most restrictive condition here is $$ d < -6 $$, as it ensures all other inequalities are also satisfied.

---

### **Final Solution:**

$$
d < -6
$$

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**Interpretation:** The value of $$ d $$ must be less than -6 to satisfy all the given inequalities.
$$ d < -6 $$

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Solución

1. Solving :

2. Other Inequalities:

3. Combining All Inequalities:

Final Solution:

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