How do you solve $\frac { x + 6} { 3} \geq x - 2$ ?

Question

1059 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-22T06:21:43

$x<=6$

Thankfully, solving inequalities is almost exactly the same as solving equations! We can approach this problem the same way.

$(x+6)/3>=x-2$

First, start off by multiplying $3$ on both sides.

$3/1*(x+6)/3>=3(x-2)$

This will cancel out the $3$ on one side.

$cancel3/1*(x+6)/cancel3>=3(x-2)$

$x+6>=3(x-2)$

Use the distributive property to simplify the right side of the inequality.

$x+6>=3x-6$

Subtract $x$ on both sides to bring all variable terms to the right side.

$6>=2x-6$

Add $6$ to both sides to bring all constants to the left side.

$12>=2x$

Last, divide by $2$ to completely isolate $x$ .

$6>=x$

Don't forget to rewrite your inequality in the correct order! You've finally arrived to your answer:

$x<=6$

How do you solve \frac { x + 6} { 3} \geq x - 2\frac { x + 6} { 3} \geq x - 2?