In Exercises 51–58, solve each compound inequality. - 11 \u003c 2x - 1 ≤ - 5

Start by writing the compound inequality as two separate inequalities combined: $$11 \u003c 2x - 1$$ and $$2x - 1 \leq -5. $$Solve the first inequality $$11 \u003c 2x - 1 by $$adding 1 to both sides to isolate the term with $$x$$: $$11 + 1 \u003c 2x$$ which simplifies to $$12 \u003c 2x. $$Next, divide both sides of $$12 \u003c 2x by 2 to $$solve for $$x$$: $$\frac{12}{2} \u003c x$$ which simplifies to $$6 \u003c x. $$Now solve the second inequality $$2x - 1 \leq -5 by $$adding 1 to both sides: $$2x \leq -5 + 1$$ which simplifies to $$2x \leq -4. $$Divide both sides of $$2x \leq -4 by 2 to $$solve for $$x$$: $$x \leq \frac{-4}{2}$$ which simplifies to $$x \leq -2.$$

Ch. 1 - Equations and Inequalities

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Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 55

Capitolo 2, Problema 55

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

Guida verificata passo dopo passo

Start by writing the compound inequality as two separate inequalities combined: $11 < 2x - 1$ and $2x - 1 \leq -5$.

Solve the first inequality $11 < 2x - 1$ by adding 1 to both sides to isolate the term with $x$: $11 + 1 < 2x$ which simplifies to $12 < 2x$.

Next, divide both sides of $12 < 2x$ by 2 to solve for $x$: $\frac{12}{2} < x$ which simplifies to $6 < x$.

Now solve the second inequality $2x - 1 \leq -5$ by adding 1 to both sides: $2x \leq -5 + 1$ which simplifies to $2x \leq -4$.

Divide both sides of $2x \leq -4$ by 2 to solve for $x$: $x \leq \frac{-4}{2}$ which simplifies to $x \leq -2$.

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