# Find the Union (or) -3(t-1)=15 or, 15+t<17

-3(t-1)=15 or, 15+t<17
Simplify the first inequality.
Divide each term by -3 and simplify.
Divide each term in -3(t-1)=15 by -3.
-3(t-1)-3=15-3 or 15+t<17
Cancel the common factor of -3.
Cancel the common factor.
-3(t-1)-3=15-3 or 15+t<17
Divide t-1 by 1.
t-1=15-3 or 15+t<17
t-1=15-3 or 15+t<17
Divide 15 by -3.
t-1=-5 or 15+t<17
t-1=-5 or 15+t<17
Move all terms not containing t to the right side of the equation.
Add 1 to both sides of the equation.
t=-5+1 or 15+t<17
t=-4 or 15+t<17
t=-4 or 15+t<17
t=-4 or 15+t<17
Move all terms not containing t to the right side of the inequality.
Subtract 15 from both sides of the inequality.
t=-4 or t<17-15
Subtract 15 from 17.
t=-4 or t<2
t=-4 or t<2
The union consists of all of the elements that are contained in each interval.
t<2
The result can be shown in multiple forms.
Inequality Form:
t<2
Interval Notation:
(-∞,2)
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Find the Union (or) -3(t-1)=15 or, 15+t<17

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