Question

Solve the following inequality problems:

please show your work

question 1 10- 3x > 1

question 2 12x - 4 ≥ 20

question 3 5x ≤ - 3x + 32

Answer 1

`\boxed{1.x < 3; \quad 2. \, x \geq 2; \quad 3.\, x \leq 4}`

Explanation:

1. 10 - 3x > 1

`\begin{array}{rcll}10 - 3x & > & 1 & \\-3x & <& -9 &\text{Subtracted 10 from each side}\\x & < & 3 &\text{Divided each side by -3}\\\end{array}`

`\text{The solution is } \boxed{\mathbf{x < 3}}`

2. 12x - 4 ≥ 20

`\begin{array}{rcll}12x - 4& \geq & 20 & \\12x & \geq& 24 & \text{Added 4 to each side}\\x & \geq & \mathbf{2} & \text{Divided each side by 12}\\\end{array}`

`\text{The solution is } \boxed{\mathbf{x \geq 2}}`

3. 5x ≤ -3x + 32

`\begin{array}{rcll}5x& \leq & -3x + 32 & \\8x & \leq& 32 & \text{Added 3x to each side}\\x & \leq & \mathbf{4} & \text{Divided each side by 8}\\\end{array}`

`\text{The solution is } \boxed{\mathbf{x \leq 4}}`