Questions: Solve for (s). [19 s-13-17 s>-9 text or s-13-5 s geq-5]

Transcript text: Solve for $s$. \[ \begin{array}{l} 19 s-13-17 s>-9 \text { or } s-13- \\ 5 s \geq-5 \end{array} \]

Solution

Solution Steps

Step 1: Solve the First Inequality

We start with the inequality $19s - 13 - 17s > -9$. Simplifying this gives us: \[ 2s - 13 > -9 \] Adding 13 to both sides results in: \[ 2s > 4 \] Dividing both sides by 2, we find: \[ s > 2 \]

Step 2: Solve the Second Inequality

Next, we solve the inequality $s - 13 - 5s \geq -5$. Simplifying this gives us: \[ -4s - 13 \geq -5 \] Adding 13 to both sides results in: \[ -4s \geq 8 \] Dividing both sides by -4 (and reversing the inequality) gives us: \[ s \leq -2 \]

Step 3: Combine the Solutions

The solutions from the two inequalities are $s > 2$ and $s \leq -2$. Therefore, the compound solution can be expressed as: \[ s \leq -2 \quad \text{or} \quad s > 2 \]

Final Answer

$\boxed{s \leq -2 \text{ or } s > 2}$

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