Respuesta :

Answer:

Problem 1: [tex]\frac{2x-3}{5}=x+6[/tex] gives x=-11

Problem 2: [tex]2x-\frac{3}{5}=x+6[/tex] gives x=33/5

Step-by-step explanation:

I will do it both ways:

Problem 1:

[tex]\frac{2x-3}{5}=x+6[/tex]

I don't like the fraction so I'm going to clear by multiplying both sides by 5:

[tex]2x-3=5(x+6)[/tex]

Distribute:

[tex]2x-3=5x+30[/tex]

Subtract 2x on both sides:

[tex]-3=3x+30[/tex]

Subtract 30 on both sides:

[tex]-33=3x[/tex]

Divide both sides by 3:

[tex]-11=x[/tex]

Problem 2:

[tex]2x-\frac{3}{5}=x+6[/tex]

Clear the fraction by multiplying both sides by 5:

[tex]5(2x-\frac{3}{5})=5(x+6)[/tex]

Distribute:

[tex]10x-3=5x+30[/tex]

Subtract 5x on both sides:

[tex]5x-3=30[/tex]

Add 3 on both sides:

[tex]5x=33[/tex]

Divide both sides by 5:

[tex]x=\frac{33}{5}[/tex]

carlosego

For this case we must solve the following equation:

[tex]\frac {2x-3} {5} = x + 6[/tex]

Multiplying by 5 on both sides we have:

[tex]2x-3 = 5 (x + 6)\\2x-3 = 5x + 30[/tex]

We add 3 to both sides of the equation:

[tex]2x = 5x + 30 + 3\\2x = 5x + 33[/tex]

Subtracting 5x on both sides:

[tex]2x-5x = 33\\-3x = 33[/tex]

Dividing between -3 on both sides:

[tex]x = \frac {33} {- 3}\\x = -11[/tex]

Answer:

-11