# How do you solve 5(x+4)<=4(2x+3)?

Nov 5, 2015

$x \ge \frac{8}{3}$ by properties of inequality.

#### Explanation:

The first step would be to distribute each number to the parenthesis. So you would have $5 x + 20 \le 8 x + 12$.

Now you can subtract $5 x$ from each side, by the subtraction property of equality (or inequality in this case). You can subtract $8 x$ from each side also, but that results in a $- x$ on one side and that makes it harder to work with later on. After this, you are left with $20 \le 3 x + 12$.

Now you want to isolate $x$ to one side, and this can be done with the subtraction property of inequality. Subtract $12$ from each side of the inequality, $8 \le 3 x$.

The next thing you want to do is to get $x$ without a coefficient. This can be done with the division property of inequality. Dividing each side by $3$, you would be left with $\frac{8}{3} \le x$. (By the symmetric property of inequality you can reverse the inequality sign and make it $x \ge \frac{8}{3}$.

$\frac{8}{3}$ can also be reduced to $2 \frac{2}{3}$ or $2.667$ (rounded to the thousandths place).