Question

- 7h + 2(-4h +5) > -4h +1 +10. Solve for h​

Answer 1

We are given with an inequality and we need to solve for h . So let's start

`{:\implies \quad \sf -7h+2(-4h+5)> -4h+1+10}`

`{:\implies \quad \sf -7h-8h+10> -4h+11}`

`{:\implies \quad \sf -15h+10> -4h+11}`

Add 4h to both sides

`{:\implies \quad \sf -15h+10+4h> \cancel{-4h}+11+\cancel{4h}}`

`{:\implies \quad \sf -11h+10> 11}`

Subtracting 10 from both sides ;

`{:\implies \quad \sf -11h+10-11> \cancel{11}-\cancel{11}}`

`{:\implies \quad \sf -11h-1> 0}`

Adding 1 to both sides

`{:\implies \quad \sf -11h-\cancel{1}+\cancel{1}> 1}`

`{:\implies \quad \sf -11h>1}`

Now dividing both sides by -11 also , when we divide or multiply an inequality by a -ve , we changes the sign too. So ;

`{:\implies \quad \sf (-11h)/(-11)< -(1)/(11)}`

`{:\implies \quad \sf h< -(1)/(11)}`

`{:\implies \quad \bf \therefore \quad \underline{\underline{h\in \left(-\infty ,-(1)/(11)\right)}}}`

Answer 2

Hello.

-7h + 2(-4h + 5) > -4h + 1 + 10 ; solve for h

Our first step is to get rid of all the parenthesis. We can do this by simplifying everything out.

-7h - 8h + 10 > -4h + 11

Add like terms.

-15h + 10 > -4h + 11

Now, we must isolate our variables. We do this by moving all variables to one side and moving our other numbers to the other.

Subtract 10 from both sides. Then, add 4h to both sides.

-15h + 4h > 11 - 10

Simplify.

-11h > 1

Divide both sides by -11.

However, keep in mind that when dividing with a negative, you must change the sign. Therefore, > turns into <

-11h ÷ -11 < 1 ÷ -11

h < 1/-11

Therefore, h < -1/11