4y+1>5 , 3y-6>12

Move all terms not containing y to the right side of the inequality.

Subtract 1 from both sides of the inequality.

4y>5-1 and 3y-6>12

Subtract 1 from 5.

4y>4 and 3y-6>12

4y>4 and 3y-6>12

Divide each term by 4 and simplify.

Divide each term in 4y>4 by 4.

4y4>44 and 3y-6>12

Cancel the common factor of 4.

Cancel the common factor.

4y4>44 and 3y-6>12

Divide y by 1.

y>44 and 3y-6>12

y>44 and 3y-6>12

Divide 4 by 4.

y>1 and 3y-6>12

y>1 and 3y-6>12

y>1 and 3y-6>12

Move all terms not containing y to the right side of the inequality.

Add 6 to both sides of the inequality.

y>1 and 3y>12+6

Add 12 and 6.

y>1 and 3y>18

y>1 and 3y>18

Divide each term by 3 and simplify.

Divide each term in 3y>18 by 3.

y>1 and 3y3>183

Cancel the common factor of 3.

Cancel the common factor.

y>1 and 3y3>183

Divide y by 1.

y>1 and y>183

y>1 and y>183

Divide 18 by 3.

y>1 and y>6

y>1 and y>6

y>1 and y>6

The intersection consists of the elements that are contained in both intervals.

y>6

The result can be shown in multiple forms.

Inequality Form:

y>6

Interval Notation:

(6,∞)

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Find the Intersection (and) 4y+1>5 , 3y-6>12