Answer :
Sure! Let's solve the problem step-by-step.
The problem states that "Thirteen more than three times [tex]\( x \)[/tex] is no more than the opposite of eleven." We need to create an inequality and solve for [tex]\( x \)[/tex].
1. Translate the verbal statement into an inequality:
- "Three times [tex]\( x \)[/tex]" can be written as [tex]\( 3x \)[/tex].
- "Thirteen more than three times [tex]\( x \)[/tex]" becomes [tex]\( 3x + 13 \)[/tex].
- "No more than the opposite of eleven" means it is less than or equal to [tex]\(-11\)[/tex].
So, the inequality is:
[tex]\[ 3x + 13 \leq -11 \][/tex]
2. Solve the inequality step-by-step:
- First, subtract 13 from both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ 3x + 13 - 13 \leq -11 - 13 \][/tex]
[tex]\[ 3x \leq -24 \][/tex]
- Next, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x \leq -8 \][/tex]
3. Final solution:
The solution to the inequality [tex]\( 3x + 13 \leq -11 \)[/tex] is that [tex]\( x \)[/tex] must be less than or equal to [tex]\(-8\)[/tex].
Thus, the solution set is:
[tex]\[ x \leq -8 \][/tex]
This means any value of [tex]\( x \)[/tex] that is [tex]\(-8\)[/tex] or less will satisfy the original condition.
The problem states that "Thirteen more than three times [tex]\( x \)[/tex] is no more than the opposite of eleven." We need to create an inequality and solve for [tex]\( x \)[/tex].
1. Translate the verbal statement into an inequality:
- "Three times [tex]\( x \)[/tex]" can be written as [tex]\( 3x \)[/tex].
- "Thirteen more than three times [tex]\( x \)[/tex]" becomes [tex]\( 3x + 13 \)[/tex].
- "No more than the opposite of eleven" means it is less than or equal to [tex]\(-11\)[/tex].
So, the inequality is:
[tex]\[ 3x + 13 \leq -11 \][/tex]
2. Solve the inequality step-by-step:
- First, subtract 13 from both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ 3x + 13 - 13 \leq -11 - 13 \][/tex]
[tex]\[ 3x \leq -24 \][/tex]
- Next, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x \leq -8 \][/tex]
3. Final solution:
The solution to the inequality [tex]\( 3x + 13 \leq -11 \)[/tex] is that [tex]\( x \)[/tex] must be less than or equal to [tex]\(-8\)[/tex].
Thus, the solution set is:
[tex]\[ x \leq -8 \][/tex]
This means any value of [tex]\( x \)[/tex] that is [tex]\(-8\)[/tex] or less will satisfy the original condition.
