Question

Solve the following inequalities 1/2 x ≥ 3

Answer 1

x
`x\geq 6`.

Explanation:

1. Write the expression.

`(1)/(2)x \geq 3`

2. Divide both sides by 1/2.

`((1)/(2))/((1)/(2) ) x\geq (3)/((1)/(2) )`

Dividing by a fraction of the same as multiplying by its multiplicative inverse. Since the multiplicative inverse of 1/2 is 2/1, we may rewrite as:

`(2)/(1) *(1)/(2) x\geq (2)/(1) *3`

3. Simplify.

`(1)x\geq(6)\\ \\x\geq6`

4. Verify.

`(1)/(2)(6) \geq 3\\ \\3\geq 3`

Correct!

5. Express the final result.

x
`x\geq 6`.