How do you solve the inequality: #3 2 (5-y) + 3 -17#?

Question

How do you solve the inequality: #3 > 2 (5-y) + 3 > -17#?

Avery Alexander · Accepted Answer

#5 < y < 15#

#3 > 10-2y+3> -17# Distribute the #2# in #2(5-y)#

#3 >13-2y> -17# Combine like terms

#-10> -2y> -30# Subtract 13 from everything

#5< y < 15# Divide through by #-2#

Remember that the inequality flips when dividing by a negative number.

Or written another way

#y> 5# and #y<15#

Julia Adams · Answer

#5 < y < 15#

You can split the given inequality into two simpler inequalities :)

from #3 > 2(5-y)+3> -17#

we can get #3>2(5-y)+3# and #2(5-y)+3> -17#

then solving each...

#3>2(5-y)+3# [distribute the 2] #3>10-2y+3# [add like terms (the 10 and 3)] #3>13-2y# [add 2y to both sides] #2y + 3 > 13# [now subtract 3 from both sides] #2y > 10# [finally, divide both sides by 2 to get y all alone] #y > 5#

#2(5-y)+3> -17# [first distribute the 2] #10-2y+3> -17# [add like terms] #13 - 2y > -17# [add 2y to both sides] #13 > 2y - 17# [add 17 to both sides] #13+17 > 2y# [simplify] #30>2y# [finally, divide both sides by 2] #y < 15#

so we get #y > 5# and #y < 15#

Avery Alexander · Answer

undefined To solve the inequality $3 > 2(5-y) + 3 > -17$: 1. Start by solving each inequality separately: - Solve $2(5-y) + 3 > -17$. - Solve $2(5-y) + 3 < 3$. 2. For $2(5-y) + 3 > -17$: - Distribute $2$ and simplify: $10 - 2y + 3 > -17$. - Combine like terms: $13 - 2y > -17$. - Subtract $13$ from both sides: $-2y > -30$. - Divide both sides by $-2$, remembering to reverse the inequality sign since dividing by a negative number: $y < 15$. 3. For $2(5-y) + 3 < 3$: - Distribute $2$ and simplify: $10 - 2y + 3 < 3$. - Combine like terms: $13 - 2y < 3$. - Subtract $13$ from both sides: $-2y < -10$. - Divide both sides by $-2$, remembering to reverse the inequality sign: $y > 5$. So, the solution to the inequality is $5 < y < 15$.

How do you solve the inequality: #3 &gt; 2 (5-y) + 3 &gt; -17#?

How do you solve the inequality: #3 > 2 (5-y) + 3 > -17#?