Answer :
Sure, let's solve the inequality step-by-step.
The problem states: "Nine more than twice a number is greater than negative eleven."
1. Let's define the unknown number as [tex]\( x \)[/tex].
2. The phrase "twice a number" can be written as [tex]\( 2x \)[/tex].
3. Adding nine to this gives us [tex]\( 2x + 9 \)[/tex].
So, the inequality we need to solve is:
[tex]\[ 2x + 9 > -11 \][/tex]
Now we need to isolate [tex]\( x \)[/tex].
4. Subtract 9 from both sides of the inequality to get rid of the constant term on the left side:
[tex]\[ 2x + 9 - 9 > -11 - 9 \][/tex]
[tex]\[ 2x > -20 \][/tex]
5. Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{2x}{2} > \frac{-20}{2} \][/tex]
[tex]\[ x > -10 \][/tex]
So, the solution to the inequality is:
[tex]\[ x > -10 \][/tex]
This means that any value of [tex]\( x \)[/tex] that is greater than -10 will satisfy the given inequality.
The problem states: "Nine more than twice a number is greater than negative eleven."
1. Let's define the unknown number as [tex]\( x \)[/tex].
2. The phrase "twice a number" can be written as [tex]\( 2x \)[/tex].
3. Adding nine to this gives us [tex]\( 2x + 9 \)[/tex].
So, the inequality we need to solve is:
[tex]\[ 2x + 9 > -11 \][/tex]
Now we need to isolate [tex]\( x \)[/tex].
4. Subtract 9 from both sides of the inequality to get rid of the constant term on the left side:
[tex]\[ 2x + 9 - 9 > -11 - 9 \][/tex]
[tex]\[ 2x > -20 \][/tex]
5. Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{2x}{2} > \frac{-20}{2} \][/tex]
[tex]\[ x > -10 \][/tex]
So, the solution to the inequality is:
[tex]\[ x > -10 \][/tex]
This means that any value of [tex]\( x \)[/tex] that is greater than -10 will satisfy the given inequality.
