Respuesta :

Answer:

x > ten sevenths

Step-by-step explanation:

We want to solve for x in the inequality:

[tex]6x+\frac{1}{4}(4x+8)>12[/tex]

We multiply through by 4 to clear the fraction.

[tex]4*6x+4*\frac{1}{4}(4x+8)>4*12[/tex]

[tex]\implies 24x+1(4x+8)>48[/tex]

[tex]\implies 24x+4x+8>48[/tex]

Group similar terms to get:

[tex]\implies 24x+4x>48-8[/tex]

[tex]\implies 28x>40[/tex]

[tex]\implies x>\frac{40}{28}[/tex]

[tex]\implies x>\frac{10*4}{7*4}[/tex]

[tex]\implies x>\frac{10}{7}[/tex]

The first choice is correct

Answer:

The correct option is 1.

Step-by-step explanation:

The given inequality is

[tex]6x+\frac{1}{4}(4x+8)>12[/tex]

We need to solve the inequality for x.

Using distributive property we get

[tex]6x+\frac{1}{4}(4x)+\frac{1}{4}(8)>12[/tex]

[tex]6x+x+2>12[/tex]

Combine like terms.

[tex]7x+2>12[/tex]

Subtract 2 from both sides.

[tex]7x>12-2[/tex]

[tex]7x>10[/tex]

Divide both sides by 7.

[tex]x>\frac{10}{7}[/tex]

x > ten sevenths

Therefore, the correct option is 1.

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