Let's consider the equation $$ |x+3|-|x-4|=x+4 $$. Simplify $$ |x+3|-|x-4| $$ and solve the initial equation if $$ x

Question

Let's consider the equation $$ |x+3|-|x-4|=x+4 $$. Simplify $$ |x+3|-|x-4| $$ and solve the initial equation if $$ x<-3 $$. Answer: Simplified expression : CLEAR ALL $$ \quad $$ List the solutions or write no solutions here : Exa

UpStudy AI · Accepted Answer

**Simplified Expression:**

For $$ x < -3 $$, we have:
$$
|x+3| = -(x+3) \quad \text{and} \quad |x-4| = -(x-4)
$$
Thus:
$$
|x+3| - |x-4| = -(x+3) - (-(x-4)) = -x-3+x-4 = -7.
$$

**Solving the Equation:**

Substitute the simplified expression into the equation:
$$
-7 = x+4
$$
Subtracting 4 from both sides gives:
$$
-11 = x
$$
So, the solution is:
$$
x = -11
$$

**List the solutions:**

$$ x = -11 $$
For $$ x < -3 $$, $$ |x+3| - |x-4| = -7 $$. Solving $$ -7 = x + 4 $$ gives $$ x = -11 $$.

Let’s consider the equation .
Simplify and solve the initial equation if .
Answer: Simplified expression :
CLEAR ALL List the solutions or write no solutions here : Exa

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Let’s consider the equation . Simplify and solve the initial equation if . Answer: Simplified expression : CLEAR ALL List the solutions or write no solutions here : Exa