Select all of the inequalities below where -11 is a solution.
[tex]3 x-1 \textless \ 32[/tex]
[tex]x+4 \geq-12[/tex]
[tex]4 x \geq 23[/tex]
[tex]-x \textless \ 12[/tex]
[tex]-10 \leq x-3[/tex]
[tex]x+2 \geq-8[/tex]
Answer (2)
3 x − 1 < 32 , x + 4 ≥ − 12 , − x < 12 .
Explanation
Problem Analysis We are given six inequalities and need to determine which ones have -11 as a solution. To do this, we will substitute x = − 11 into each inequality and check if the resulting statement is true.
Checking Inequality 1
Inequality 1: 3 x − 1 < 32 Substitute x = − 11 : 3 ( − 11 ) − 1 < 32 Simplify: − 33 − 1 < 32 − 34 < 32 . This is true, so -11 is a solution.
Checking Inequality 2
Inequality 2: x + 4 ≥ − 12 Substitute x = − 11 : − 11 + 4 ≥ − 12 Simplify: − 7 ≥ − 12 . This is true, so -11 is a solution.
Checking Inequality 3
Inequality 3: 4 x ≥ 23 Substitute x = − 11 : 4 ( − 11 ) ≥ 23 Simplify: − 44 ≥ 23 . This is false, so -11 is not a solution.
Checking Inequality 4
Inequality 4: − x < 12 Substitute x = − 11 : − ( − 11 ) < 12 Simplify: 11 < 12 . This is true, so -11 is a solution.
Checking Inequality 5
Inequality 5: − 10 ≤ x − 3 Substitute x = − 11 : − 10 ≤ − 11 − 3 Simplify: − 10 ≤ − 14 . This is false, so -11 is not a solution.
Checking Inequality 6
Inequality 6: x + 2 ≥ − 8 Substitute x = − 11 : − 11 + 2 ≥ − 8 Simplify: − 9 ≥ − 8 . This is false, so -11 is not a solution.
Final Answer Therefore, the inequalities for which -11 is a solution are: 3 x − 1 < 32 x + 4 ≥ − 12 − x < 12
Examples
Understanding inequalities helps in various real-life scenarios, such as budgeting. For instance, if you have a limited amount to spend each month, you can use inequalities to determine how much you can allocate to different categories like food, rent, and entertainment while staying within your budget. Similarly, in cooking, inequalities can help you adjust ingredient quantities to achieve a desired taste or nutritional value. These mathematical tools provide a framework for making informed decisions and managing resources effectively.
The inequalities where -11 is a solution are 3 x − 1 < 32 , x + 4 ≥ − 12 , and − x < 12 . These inequalities are validated by substituting -11 into each and confirming the results. The other inequalities do not hold true when substituting -11.
;
