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.