Resolver las siguientes inecuaciones lineales.
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Ask by Rogers Lawson. in Colombia

Mar 20,2025

Question

Resolver las siguientes inecuaciones lineales. a. $$ 2 x-1<6 $$ b. $$ 3 x-5<7 $$ c. $$ 2 x+1>x-4 $$ d. $$ 3 x+1 \geq 4 x-3 $$ e. $$ \frac{2 x-5}{4} \leq 3 $$ f. $$ \frac{2 x-9}{7}>0 $$ g. $$ \frac{2 x-5}{3}\frac{4 x-5}{-3} $$ i $$ 1<\frac{4 x-1}{5}<5 \quad 1<\frac{4 x-1}{-3}<5 $$

UpStudy AI · Accepted Answer

Solve the inequality by following steps: - step0: Solve for $$x$$: $$3x-5<7$$ - step1: Move the constant to the right side: $$3x<7+5$$ - step2: Add the numbers: $$3x<12$$ - step3: Divide both sides: $$\frac{3x}{3}<\frac{12}{3}$$ - step4: Divide the numbers: $$x<4$$ Solve the equation $$ (2x-5)/4 <= 3 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$\frac{\left(2x-5 ight)}{4}\leq 3$$ - step1: Remove the parentheses: $$\frac{2x-5}{4}\leq 3$$ - step2: Multiply both sides: $$\frac{2x-5}{4} imes 4\leq 3 imes 4$$ - step3: Multiply the terms: $$2x-5\leq 12$$ - step4: Move the constant to the right side: $$2x\leq 12+5$$ - step5: Add the numbers: $$2x\leq 17$$ - step6: Divide both sides: $$\frac{2x}{2}\leq \frac{17}{2}$$ - step7: Divide the numbers: $$x\leq \frac{17}{2}$$ Solve the equation $$ 1<(4x-1)/-3<5 $$. Solve the system of inequalities by following steps: - step0: Solve for $$x$$: $$\left\{ \begin{array}{l}1<\frac{\left(4x-1 ight)}{\left(-3 ight)}\\frac{\left(4x-1 ight)}{\left(-3 ight)}<5\end{array} ight.$$ - step1: Remove the parentheses: $$\left\{ \begin{array}{l}1<\frac{4x-1}{-3}\\frac{4x-1}{-3}<5\end{array} ight.$$ - step2: Solve the inequality: $$\left\{ \begin{array}{l}x<-\frac{1}{2}\x>-\frac{7}{2}\end{array} ight.$$ - step3: Find the intersection: $$-\frac{7}{2}0 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$\frac{\left(2x-9 ight)}{7}>0$$ - step1: Remove the parentheses: $$\frac{2x-9}{7}>0$$ - step2: Multiply both sides: $$\frac{2x-9}{7} imes 7>0 imes 7$$ - step3: Multiply the terms: $$2x-9>0$$ - step4: Move the constant to the right side: $$2x>0+9$$ - step5: Remove 0: $$2x>9$$ - step6: Divide both sides: $$\frac{2x}{2}>\frac{9}{2}$$ - step7: Divide the numbers: $$x>\frac{9}{2}$$ Solve the equation $$ (2x-5)/3-8$$ Solve the equation $$ 10-3x>(4x-5)/-3 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$10-3x>\frac{\left(4x-5 ight)}{\left(-3 ight)}$$ - step1: Remove the parentheses: $$10-3x>\frac{4x-5}{-3}$$ - step2: Rewrite the fraction: $$10-3x>-\frac{4x-5}{3}$$ - step3: Multiply both sides: $$\left(10-3x ight) imes 3>-\frac{4x-5}{3} imes 3$$ - step4: Multiply the terms: $$30-9x>-4x+5$$ - step5: Move the expression to the left side: $$-9x+4x>5-30$$ - step6: Add and subtract: $$-5x>5-30$$ - step7: Add and subtract: $$-5x>-25$$ - step8: Change the signs: $$5x<25$$ - step9: Divide both sides: $$\frac{5x}{5}<\frac{25}{5}$$ - step10: Divide the numbers: $$x<5$$ Solve the equation $$ 2x+1>x-4 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$2x+1>x-4$$ - step1: Move the expression to the left side: $$2x-x>-4-1$$ - step2: Add and subtract: $$x>-4-1$$ - step3: Add and subtract: $$x>-5$$ Solve the equation $$ 1<(4x-1)/5<5 $$. Solve the system of inequalities by following steps: - step0: Solve for $$x$$: $$\left\{ \begin{array}{l}1<\frac{\left(4x-1 ight)}{5}\\frac{\left(4x-1 ight)}{5}<5\end{array} ight.$$ - step1: Remove the parentheses: $$\left\{ \begin{array}{l}1<\frac{4x-1}{5}\\frac{4x-1}{5}<5\end{array} ight.$$ - step2: Solve the inequality: $$\left\{ \begin{array}{l}x>\frac{3}{2}\x<\frac{13}{2}\end{array} ight.$$ - step3: Find the intersection: $$\frac{3}{2}=4x-3 $$. Solve the inequality by following steps: - step0: Solve for $$x$$: $$3x+1\geq 4x-3$$ - step1: Move the expression to the left side: $$3x-4x\geq -3-1$$ - step2: Add and subtract: $$-x\geq -3-1$$ - step3: Add and subtract: $$-x\geq -4$$ - step4: Change the signs: $$x\leq 4$$ Aquí están las soluciones para las inecuaciones lineales que proporcionaste: a. $$ 2x - 1 < 6 $$ Solución: $$ x < \frac{7}{2} $$ b. $$ 3x - 5 < 7 $$ Solución: $$ x < 4 $$ c. $$ 2x + 1 > x - 4 $$ Solución: $$ x > -5 $$ d. $$ 3x + 1 \geq 4x - 3 $$ Solución: $$ x \leq 4 $$ e. $$ \frac{2x - 5}{4} \leq 3 $$ Solución: $$ x \leq \frac{17}{2} $$ f. $$ \frac{2x - 9}{7} > 0 $$ Solución: $$ x > \frac{9}{2} $$ g. $$ \frac{2x - 5}{3} < x + 1 $$ Solución: $$ x > -8 $$ h. $$ 6x - 1 < \frac{5x - 1}{3} $$ Solución: $$ x < \frac{2}{13} $$ i. $$ 10 - 3x > \frac{4x - 5}{-3} $$ Solución: $$ x < 5 $$ j. $$ 1 < \frac{4x - 1}{5} < 5 $$ Solución: $$ \frac{3}{2} < x < \frac{13}{2} $$ k. $$ 1 < \frac{4x - 1}{-3} < 5 $$ Solución: $$ -\frac{7}{2} < x < -\frac{1}{2} $$ Si necesitas más ayuda o aclaraciones, no dudes en preguntar. a. $$ x < \frac{7}{2} $$ b. $$ x < 4 $$ c. $$ x > -5 $$ d. $$ x \leq 4 $$ e. $$ x \leq \frac{17}{2} $$ f. $$ x > \frac{9}{2} $$ g. $$ x > -8 $$ h. $$ x < \frac{2}{13} $$ i. $$ x < 5 $$ j. $$ \frac{3}{2} < x < \frac{13}{2} $$ k. $$ -\frac{7}{2} < x < -\frac{1}{2} $$

Resolver las siguientes inecuaciones lineales.
a.
b.
c.
d.
e.
f.
g.
h.
i.
i

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