Respuesta :

loneguy

[tex]5\sqrt{3x+1} = 10\\\\\implies \sqrt{3x+1} = \dfrac{10}5 \\\\\implies \sqrt{3x+1} = 2 \\\\\implies 3x +1 = 4\\\\\implies 3x = 4-1 \\\\\implies 3x = 3\\\\\implies x =1[/tex]

Answer:

x = 1

Step-by-step explanation:

Given equation:

[tex]\dfrac{5(3x+1)^1}{2} =10[/tex]

If a term has "1" as it's exponent, it means that it's the number itself. Therefore, we can remove the "exponent".

[tex]:\implies\dfrac{5(3x+1)}{2} =10[/tex]

Simplify the distributive property:

[tex]:\implies\dfrac{15x+5}{2} =10[/tex]

Using cross multiplication:

[tex]:\implies15x+5} =10 \times 2[/tex]

Simplify the R.H.S:

[tex]:\implies15x+5} =20[/tex]

Subtract 5 both sides:

[tex]:\implies15x+5 - 5} =20 - 5[/tex]

Simplify both sides:

[tex]:\implies15x} =15[/tex]

Divide 15 both sides:

[tex]:\implies\dfrac{15x}{15} } =\dfrac{15}{15}[/tex]

Simplify both sides:

[tex]:\implies x= 1[/tex]