Resuelve las siguientes ecuaciones algebraicas: $$ \begin{array}{l} ext { a. } \frac{x-1}{6}-\frac{x-3}{2}=-1 \quad ext { b. } \frac{3}{4}(2 x+4)=x+19 \ ext { 6) } 4(x-10)=-6(2-x)-6 x \quad ext { d. } \frac{x-1}{4}-\frac{x-5}{36}=\frac{x+5}{9} \ ext { e. } \frac{5}{x-7}=\frac{3}{x-2}\end{array} $$

Question

Resuelve las siguientes ecuaciones algebraicas: $$ \begin{array}{l}	ext { a. } \frac{x-1}{6}-\frac{x-3}{2}=-1 \quad 	ext { b. } \frac{3}{4}(2 x+4)=x+19 \ 	ext { 6) } 4(x-10)=-6(2-x)-6 x \quad 	ext { d. } \frac{x-1}{4}-\frac{x-5}{36}=\frac{x+5}{9} \ 	ext { e. } \frac{5}{x-7}=\frac{3}{x-2}\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ \frac{x-1}{6}-\frac{x-3}{2}=-1 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x-1}{6}-\frac{x-3}{2}=-1$$
- step1: Multiply both sides of the equation by LCD:
  $$\left(\frac{x-1}{6}-\frac{x-3}{2}ight)	imes 6=-6$$
- step2: Simplify the equation:
  $$-2x+8=-6$$
- step3: Move the constant to the right side:
  $$-2x=-6-8$$
- step4: Subtract the numbers:
  $$-2x=-14$$
- step5: Change the signs:
  $$2x=14$$
- step6: Divide both sides:
  $$\frac{2x}{2}=\frac{14}{2}$$
- step7: Divide the numbers:
  $$x=7$$
Solve the equation $$ \frac{3}{4}(2x+4)=x+19 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{3}{4}\left(2x+4ight)=x+19$$
- step1: Multiply the terms:
  $$\frac{3}{2}x+3=x+19$$
- step2: Multiply both sides of the equation by LCM:
  $$\left(\frac{3}{2}x+3ight)	imes 2=\left(x+19ight)	imes 2$$
- step3: Calculate:
  $$3x+6=\left(x+19ight)	imes 2$$
- step4: Calculate:
  $$3x+6=2x+38$$
- step5: Move the expression to the left side:
  $$3x-2x=38-6$$
- step6: Add and subtract:
  $$x=38-6$$
- step7: Add and subtract:
  $$x=32$$
Solve the equation $$ 4(x-10)=-6(2-x)-6x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$4\left(x-10ight)=-6\left(2-xight)-6x$$
- step1: Subtract the terms:
  $$4\left(x-10ight)=-12$$
- step2: Divide both sides:
  $$\frac{4\left(x-10ight)}{4}=\frac{-12}{4}$$
- step3: Divide the numbers:
  $$x-10=-3$$
- step4: Move the constant to the right side:
  $$x=-3+10$$
- step5: Add the numbers:
  $$x=7$$
Solve the equation $$ \frac{x-1}{4}-\frac{x-5}{36}=\frac{x+5}{9} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x-1}{4}-\frac{x-5}{36}=\frac{x+5}{9}$$
- step1: Multiply both sides of the equation by LCD:
  $$\left(\frac{x-1}{4}-\frac{x-5}{36}ight)	imes 36=\frac{x+5}{9}	imes 36$$
- step2: Simplify the equation:
  $$8x-4=4x+20$$
- step3: Move the expression to the left side:
  $$8x-4x=20+4$$
- step4: Add and subtract:
  $$4x=20+4$$
- step5: Add and subtract:
  $$4x=24$$
- step6: Divide both sides:
  $$\frac{4x}{4}=\frac{24}{4}$$
- step7: Divide the numbers:
  $$x=6$$
Solve the equation $$ \frac{5}{x-7}=\frac{3}{x-2} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{5}{x-7}=\frac{3}{x-2}$$
- step1: Find the domain:
  $$\frac{5}{x-7}=\frac{3}{x-2},x \in \left(-\infty,2ight)\cup \left(2,7ight)\cup \left(7,+\inftyight)$$
- step2: Cross multiply:
  $$5\left(x-2ight)=\left(x-7ight)	imes 3$$
- step3: Simplify the equation:
  $$5\left(x-2ight)=3\left(x-7ight)$$
- step4: Calculate:
  $$5x-10=3\left(x-7ight)$$
- step5: Calculate:
  $$5x-10=3x-21$$
- step6: Move the expression to the left side:
  $$5x-10-\left(3x-21ight)=0$$
- step7: Calculate:
  $$2x+11=0$$
- step8: Move the constant to the right side:
  $$2x=0-11$$
- step9: Remove 0:
  $$2x=-11$$
- step10: Divide both sides:
  $$\frac{2x}{2}=\frac{-11}{2}$$
- step11: Divide the numbers:
  $$x=-\frac{11}{2}$$
- step12: Check if the solution is in the defined range:
  $$x=-\frac{11}{2},x \in \left(-\infty,2ight)\cup \left(2,7ight)\cup \left(7,+\inftyight)$$
- step13: Find the intersection:
  $$x=-\frac{11}{2}$$
Las soluciones a las ecuaciones dadas son:

a. $$ x = 7 $$

b. $$ x = 32 $$

c. $$ x = 7 $$

d. $$ x = 6 $$

e. $$ x = -\frac{11}{2} $$ o $$ x = -5.5 $$
Las soluciones a las ecuaciones son: a. $$ x = 7 $$ b. $$ x = 32 $$ c. $$ x = 7 $$ d. $$ x = 6 $$ e. $$ x = -5.5 $$

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