# 7-8x >19-7 please answer this on how to solve the inequality?

Apr 24, 2018

$x < - \frac{5}{8}$

#### Explanation:

Isolate x.

$7 - 8 x > 19 - 7$

Add $7$ to $- 7$ to cancel it out because it is the lowest number here.

But you do to one side what you do to the other, so add $7$ to the positive $7$ on the other side. You should now have:

$14 - 8 x > 19$

Now, subtract $14$ from $14$ to cancel it out and do the same to the other side $\left(19\right)$. Now, you should have:

$- 8 x > 5$

Now, to isolate $x ,$ divide by $- 8$.

But remember when you divide or multiply an inequality by a negative value, the sign changes around.

$\frac{- 8 x}{- 8} < \frac{5}{- 8}$

Because you divided by a negative, the sign flips:

$x < - \frac{5}{8}$

Apr 24, 2018

$x < - \frac{5}{8}$

#### Explanation:

You can treat an inequality in exactly the same way as an equation, except if you multiply or divide by a negative value, the inequality sign changes around.

$7 \textcolor{b l u e}{- 8 x} > 19 - 7$

Let's avoid the problem with a negative term with the variable by moving it to the other side,

Add $8 x$ to both sides and simplify where possible:

$7 \cancel{- 8 x} \cancel{+ 8 x} > 12 \textcolor{b l u e}{+ 8 x}$

Subtract $12$ from both sides:

$7 - 12 > 12 + 8 x - 12$

$- 5 > 8 x$

-5/8 > x" "larr (div 8 on both sides)

This can be written as $x < - \frac{5}{8}$