# Thread: Interval Notation Check

1. ## Interval Notation Check

Solve the compound inequality:
3x >= -4x+2 and 5 >= 3x-4

Could someone check my work I am not sure if my interval notation is right.
My solution:
x>=2/7 & x<3

Give the result in interval notation:
(-∞,∞)

2. If $\displaystyle x\geq 2/7 \,\,and \,\,x\leq 3$, then wouldn't $\displaystyle 2/7\leq x \leq 3$, so the interval would be $\displaystyle (2/7, 3)$

3. Originally Posted by Maxwell
Solve the compound inequality:
3x >= -4x+2 and 5 >= 3x-4

Could someone check my work I am not sure if my interval notation is right.
My solution:
x>=2/7 & x<3

Give the result in interval notation:
(-∞,∞)
$\displaystyle 3x \geq -4x + 2$

$\displaystyle 7x \geq 2$

$\displaystyle x \geq \frac{2}{7}$

$\displaystyle \frac{2}{7} \leq x$.

$\displaystyle 5 \geq 3x - 4$

$\displaystyle 9 \geq 3x$

$\displaystyle 3 \geq x$

$\displaystyle x \leq 3$.

Putting the inequalities together, we get

$\displaystyle \frac{2}{7} \leq x \leq 3$.

In interval notation this is

$\displaystyle x \in [\frac{2}{7},3]$.

You have to use the square brackets because you CAN include the endpoints.