Solve for $y$:
$-5 y+8=-3 y+10$
Answer (1)
Add 5 y to both sides: 8 = 2 y + 10 .
Subtract 10 from both sides: − 2 = 2 y .
Divide both sides by 2 : y = − 1 .
The solution is − 1 .
Explanation
Understanding the Problem We are given the equation − 5 y + 8 = − 3 y + 10 and we want to solve for y . This means we want to isolate y on one side of the equation.
Adding 5 y to Both Sides First, let's add 5 y to both sides of the equation to get the y terms on the right side: − 5 y + 8 + 5 y = − 3 y + 10 + 5 y
8 = 2 y + 10
Subtracting 10 from Both Sides Next, subtract 10 from both sides to isolate the term with y :
8 − 10 = 2 y + 10 − 10 − 2 = 2 y
Dividing by 2 Finally, divide both sides by 2 to solve for y :
2 − 2 = 2 2 y − 1 = y
Final Answer Therefore, the solution is y = − 1 .
Examples
Solving linear equations like this is useful in many real-world scenarios. For example, imagine you are comparing two cell phone plans. Plan A costs $8 per month plus $5 per gigabyte of data, while Plan B costs $10 per month plus 3 p er g i g ab y t eo fd a t a . B yse tt in gu p an e q u a t i o n l ik e t h eo n e w e j u s t so l v e d , yo u c an d e t er min e h o w man y g i g ab y t eso fd a t a yo u w o u l d n ee d t o u se f or t h e tw o pl an s t ocos tt h es am e am o u n t . I n t hi sc a se , i f y$ represents the number of gigabytes, the equation would be 8 + 5 y = 10 + 3 y . Solving for y would tell you the data usage at which both plans cost the same.
