Question

-1/2x + 6 < 4x - 3
i need to find the value of X with step-by-step explanation

Answer 1

x > 2

Explanation:

-1/2x + 6 < 4x - 3

Start by adding 1/2x to both sides to get both x's on the same side

6 < 4 1/2x - 3

Add 3 to both sides to keep the x's by themselves on one side

9 < 4 1/2x

Divide both sides by 4 1/2 to get x by itself

2 < x so x > 2

Answer 2

`\boxed{\boxed{\tt x>2}}`

Explanation:

`\tt -\cfrac{1}{2}x+6<4x-3`

Subtract 6 from both sides:

• 
  `\tt -\cfrac{1}{2}x+6-6<4x-3-6`

• 
  `\tt -\cfrac{1}{2}x<4x-9`

Now, subtract 4x from both sides:

• 
  `\tt -\cfrac{1}{2}x-4x<4x-9-4x`

• 
  `\tt -\cfrac{9}{2}x<-9`

Multiply both sides by -1:

• 
  `\tt -\cfrac{9}{2}x* -1<-9* -1`

• 
  `\tt \cfrac{9}{2}x>9`

Multiply both sides by 2:

• 
  `\tt 2* \cfrac{9}{2}x>9* \:2`

• 
  `\tt 9x>18`

Divide both sides by 9:

• 
  `\tt \cfrac{9x}{9}>\cfrac{18}{9}`

• 
  `\tt x>2`

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