\(\displaystyle 3 (x-3) > 4(x+2)\)

Begin by simplifying the inequality by using the distributive property.

\(\displaystyle 3x - 9 > 4x +8\)

Add \(\displaystyle 9\) to both sides.

\(\displaystyle 3x-9 + 9 > 4x + 8 + 9\)

\(\displaystyle 3x> 4x + 17\)

Subtract \(\displaystyle 4x\) from both sides.

\(\displaystyle 3x-4x > 4x-4x+17\)

\(\displaystyle -x > 17\)

Because there is a negative variable, multiply both sides by \(\displaystyle -1\) and switch the inequality sign to its opposite.

\(\displaystyle x< -17\)

\(\displaystyle b - 6 > 13\)

Add 6 to both sides of the inequality.

\(\displaystyle b-6 + 6> 13 + 6\)

\(\displaystyle b> 19\)

\(\displaystyle -3x-12> 15\)

To isolate the variable, add \(\displaystyle 12\) to both sides of the inequality.

\(\displaystyle -3x-12+12 > 15 + 12\)

\(\displaystyle -3x >27\)

Divide both sides by \(\displaystyle -3.\) Because you are dividing by a negative integer, you have to flip or switch the inequality sign to its opposite.

\(\displaystyle x < -9\)

\(\displaystyle 12+n\leq 4\)

To isolate the variable , subtract \(\displaystyle 12\) from both sides of the inequality.

\(\displaystyle (12-12) + n \leq4-12\)

\(\displaystyle n\leq -8\)

\(\displaystyle x + 0.8\leq -0.5\)

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

\(\displaystyle x>-3/7\)