# How do you solve  -x / 7 + 4 ≥ 3x?

Jun 19, 2018

$x \le \frac{14}{11} \text{ or } x \le 1 \frac{3}{11}$

#### Explanation:

Given: $- \frac{x}{7} + 4 \ge 3 x$

The easiest way to start is to get rid of the fraction by multiplying the whole inequality by $7$:

$- \frac{x}{\cancel{7}} \cdot \frac{\cancel{7}}{1} + 4 \cdot 7 \ge 3 x \cdot 7$

$- x + 28 \ge 21 x$

Add $x$ to both sides: $\text{ } 28 \ge 22 x$

Divide by $22$: $\text{ } \frac{28}{22} \ge x$

Reduce the fraction: $\text{ } \frac{14}{11} \ge x$

This means $x \le \frac{14}{11} \text{ or } x \le 1 \frac{3}{11}$

Jun 19, 2018

$x \le \frac{14}{11}$

#### Explanation:

To get rid of the $7$ in the denominator, we can multiply all terms by $7$. This leaves us with

$- x + 28 \ge 21 x$

Since we did the same thing to both sides, we did not inadvertently change the meaning of this equation.

What we can do next is add $x$ to both sides. We get

$22 x \le 28$

Dividing both sides by $22$ gives us

$x \le \frac{28}{22}$

which can be simplified as

$x \le \frac{14}{11}$

Hope this helps!