$\displaystyle x + 0.8\leq -0.5$

To isolate the variable, subtract $\displaystyle 0.8$ from both sides of the inequality.

$\displaystyle x + 0.8-0.8 \leq -0.5-0.8$

$\displaystyle x\leq -1.3$

$\displaystyle 8x-10 > 4x-6$

Subtract $\displaystyle 4x$ from both sides of the equation

$\displaystyle 8x-4x-10 > 4x-4x-6$

$\displaystyle 4x -10> -6$

Add $\displaystyle 10$ to both sides of the equation.

$\displaystyle 4x-10 + 10 = -6 + 10$

$\displaystyle 4x > 4$

Divide both sides by 4.

$\displaystyle \frac{4x}{4} >\frac{4}{4}$

$\displaystyle x>1$

$\displaystyle 0.6x + 1.2 > 4.8$

$\displaystyle 10 (0.6x +1.2) > 4.8 (10)$

$\displaystyle 6x + 12 > 48$

$\displaystyle 6x + 12 - 12 = 48 -12$

$\displaystyle 6x > 36$

$\displaystyle \frac{6x}{6}> \frac{36}{6}$

$\displaystyle x> 6$

$\displaystyle 12\left ( \frac{x+3}{2} -\frac{3x-2}{4}\right ) < 12x-1$

$\displaystyle 12\left ( \frac{2x+6}{4} -\frac{3x-2}{4}\right ) < 12x-1$

$\displaystyle 12\left ( \frac{-x+8}{4}\right ) < 12x-1$

$\displaystyle 3(-x+8) < 12x-1$

$\displaystyle -3x +24 < 12x-1$

$\displaystyle 25 < 15x$

$\displaystyle x>\frac{25}{15} \rightarrow x>\frac{5}{3}$

Step 1: Move the constant from the left side to the right side. We have $\displaystyle -3$, so we will add 3 to both sides of the equation to move the constant over.

$\displaystyle 2x-3+(3)\leqslant9+3\rightarrow 2x\leqslant12$

Step 2: Divide by the coefficient in front of x.

$\displaystyle \frac {2x}{2}\leqslant \frac {12}{2}\rightarrow x\leqslant 6$

The values of x that satisfy the equation are $\displaystyle x\leqslant6$ (or $\displaystyle x\leq6$)

This problem involves solving the inequality. 

$\displaystyle 7+4x>-3x+4$

Add 3x to both sides

$\displaystyle 7+7x>+4$

Subtract 7 to each side

$\displaystyle 7x>-3$

divide both sides by7

$\displaystyle x>-3/7$

To solve this inequality you must first break apart the inequality into two seperate inequalities.

$\displaystyle 31>7x+3$

subtract the three from both sides

$\displaystyle 28>7x$

divide seven on both sides

$\displaystyle 4>x$

$\displaystyle 7x+3>2x+6$

subtract 2x from both sides

$\displaystyle 5x+3>6$

Subtract 3 from both sides

$\displaystyle 5x>3$

Divide by 5 on both sides

$\displaystyle 5x>3$

$\displaystyle 3x-12>-9\ Add\ 12\ to\ both\ sides\\ \\$

$\displaystyle 3x>3\ divide\ both\ sides\ by\ 3$

$\displaystyle x>1$

$\displaystyle 5-2x>13\ subtract\ 5\ from\ both\ sides$

$\displaystyle -2x>8\ divide\ both\ sides\ by\ (-2)$

$\displaystyle x< -4\ when\ dividing\ by\ a\ negative\ make\ sure\ you\ flip\ the\ inequality\ sign$

$\displaystyle We\ flip\ the\ inequality\ sign\ because\ the\ sign\ on\ both\ sides\ changed.$

$\displaystyle 4x + 12 < x + 21$

Subtract 12 from both sides of the inequality.

$\displaystyle 4x + 12 - 12< x + 21 - 12$

$\displaystyle 4x < x + 9$

Subtract $\displaystyle x$ from both sides of the inequality.

$\displaystyle 4x - x< x-x -9$

$\displaystyle 3x < 9$

Divide both sides by 3.

$\displaystyle \frac{3x}{3} < \frac{9}{3}$

$\displaystyle x < 3$