Question

For each inequality, choose the statement that describes its solution. If applicable, give the solution.a) -2(w+5)+24<2(7-w)__ no solution__ w<____ w>____ all real numbers are solutions b) 2(5v+7) greater than or equal to 10v+10 __ no solution__ v<____ v>____ all real numbers are solutions

Answer 1

a) No solution exists

b) All real numbers are solutions

Step-by-step explanation:

a) Given the inequality

`-2(w+5)+24<2(7-w)`

Simplify it.

`\begin{gathered} -2w-10+24<14-2w \\ -2w+14<14-2w \end{gathered}`

that is, 14 - 2w < 14 - 2w, which is not possible. Hence the given inequality has no solution.

b) Given the inequality

`2(5v+7)\ge10v+10`

Open the brackets.

`10v+14\ge10v+10`

Subtract 10v on both sides.

`\begin{gathered} 10v+14-10v\ge10v+10-10v \\ 14\ge10 \end{gathered}`

which is true. Hence all real numbers are solutions.