Question

Solve the inequality and tell weather it has infinite

or no solutions
`(3)/(4)x+(3)/(4)-(1)/(2)x \geq -1`

Answer 1

`[-7,+\infty)`

Explanation:

Inequalities

Solve the inequality:

`\displaystyle (3)/(4)x+(3)/(4)-(1)/(2)x \ge -1`

Joining like terms:

`\displaystyle \left((3)/(4)-(1)/(2)\right) x+(3)/(4) \ge -1`

`\displaystyle (1)/(4)x+(3)/(4) \ge -1`

Subtracting 3/4:

`\displaystyle (1)/(4)x \ge -1-(3)/(4)`

Operating:

`\displaystyle (1)/(4)x \ge -(7)/(4)`

Multiply by 4:

`x \ge -7`

The solution expressed in interval form is:

`\boxed{[-7,+\infty)}`