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- $7x-50\leq -1$ $\quad \maroonC{\text{ AND}} \quad$ $-6x+70>-2$

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Function transformation rules

Full solution

Q. -

7x-50\leq -1

\quad \maroonC{\text{ AND}} \quad

-6x+70>-2

Isolate x: To solve the first inequality $-7x - 50 \leq -1$ , we need to isolate x. We start by adding $50$ to both sides of the inequality. $\newline$ $-7x - 50 + 50 \leq -1 + 50$ $\newline$ $-7x \leq 49$
Divide by $-7$ : Now we divide both sides by $-7$ to solve for $x$ . Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign. $\newline$ $-7x / -7 \geq 49 / -7$ $\newline$ $x \geq -7$
Subtract $70$ : Next, we solve the second inequality $-6x + 70 > -2$ . We start by subtracting $70$ from both sides of the inequality. $\newline$ $-6x + 70 - 70 > -2 - 70$ $\newline$ $-6x > -72$
Divide by $-6$ : Now we divide both sides by $-6$ to solve for $x$ . Again, we must reverse the inequality sign because we are dividing by a negative number. $\newline$ $\frac{-6x}{-6} < \frac{-72}{-6}$ $\newline$ $x < 12$
Form System: We now have two inequalities that form our system: $\newline$ $x \geq -7$ (from the first inequality) $\newline$ $x < 12$ (from the second inequality) $\newline$ The solution set is the intersection of these two inequalities, which is the set of all $x$ values that satisfy both conditions simultaneously.
Find Intersection: The intersection of the two inequalities is the set of $x$ values that are greater than or equal to $-7$ and less than $12$ . This can be written in interval notation as $[-7, 12)$ .

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