To solve the inequalities \(5 + 5x < 35\) and \(2x - 4 \leq -14\), we will solve each inequality separately.
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First Inequality:
\[ 5 + 5x < 35 \] Subtract 5 from both sides: \[ 5x < 30 \] Now, divide both sides by 5: \[ x < 6 \] -
Second Inequality:
\[ 2x - 4 \leq -14 \] Add 4 to both sides: \[ 2x \leq -10 \] Now, divide both sides by 2: \[ x \leq -5 \]
Now, we combine the results of the two inequalities:
- From the first inequality, we have \(x < 6\).
- From the second inequality, we have \(x \leq -5\).
Since we are looking for the union of the two inequalities (\( \text{or} \)), the final solution is: \[ x < 6 \quad \text{or} \quad x \leq -5 \]
In interval notation, the solution is: \[ (-\infty, -5] \cup (-\infty, 6) \]
Thus, the complete solution is: \[ x < 6 \quad \text{or} \quad x \leq -5 \]