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

4y+1>5 , 3y-6>12
Simplify the first inequality.
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
Simplify the second inequality.
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
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

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