Question

Solve for b: 4b-3(2b-6)>3-(5b+9)

Answer 1

b > -8

Explanation:

Given inequality:

`4b-3(2b-6) > 3-(5b+9)`

To solve for b, begin by expanding the brackets on the left side of the inequality:

`4b-3 \cdot 2b -3 \cdot (-6) > 3-(5b+9)`

`4b-6b +18 > 3-(5b+9)`

Distribute the negative sign inside the parentheses on the right side:

`4b-6b +18 > 3-5b-9`

Combine like terms on both sides of the inequality:

`-2b +18 > -5b-6`

Add 5b to both sides:

`-2b +18 +5b > -5b-6+5b`

`3b+18 > -6`

Subtract 18 from both sides:

`3b+18-18 > -6-18`

`3b > -24`

Divide both sides by 3 to isolate b:

`(3b)/(3) > (-24)/(3)`

`b > -8`

Therefore, the solution to the given inequality is:

`\large\boxed{\boxed{b > -8}}`