Question

Solve the following inequalities:2x+7-3x<108x+2>105(x-3)>15

Answer 1

We are given the following inequalities to solve:

`\begin{gathered} 1.)\: 2x+7-3x<10 \\ 2.)\: 8x+2>10 \\ 3.)\: 5\mleft(x-3\mright)>15 \end{gathered}`

Let us solve them one by one.

The goal is to separate the variable x.

1.)

`\begin{gathered} 2x+7-3x<10 \\ 2x-3x+7<10 \\ -x+7<10 \\ -x<10-7 \\ -x<3 \\ x>-3 \end{gathered}`

When you multiply the inequality by a negative number then the direction of the inequality changes.

2.)

`\begin{gathered} 8x+2>10 \\ 8x>10-2 \\ 8x>8 \\ x>(8)/(8) \\ x>1 \end{gathered}`

3.)

`\begin{gathered} 5(x-3)>15 \\ (x-3)>(15)/(5) \\ x-3>3 \\ x>3+3 \\ x>6 \end{gathered}`

Therefore, the solution of the given inequalities is

`\begin{gathered} 1.)\: x>-3 \\ 2.)\: x>1 \\ 3.)\: x>6 \end{gathered}`