To solve, we must first multiply each side by -1. Multiplying (or dividing) by the negative flips the inequality sign:

\(\displaystyle \frac{x-1}{5}>-7\)

Now, we isolate x by multiplying by 5 and adding 1 to both sides:

\(\displaystyle x-1>-35\)

\(\displaystyle x>-34\)

Add nine on both sides.

\(\displaystyle 2z-9+9>54+9\)

Simplify both sides.

\(\displaystyle 2z>63\)

Divide by two on both sides.

\(\displaystyle \frac{2z}{2}>\frac{63}{2}\)

It is not necessary to change the sign.

The answer is:  \(\displaystyle z>\frac{63}{2}\)

Subtract 4 from both sides of the equation.

\(\displaystyle -3x+4-4\geq 35-4\)

Simplify both sides.

\(\displaystyle -3x\geq 31\)

Divide both sides by negative three.  Since we are dividing by a negative number, we will need to switch the direction of the sign.

\(\displaystyle \frac{-3x}{-3}\leq \frac{31}{-3}\)

The answer is:  \(\displaystyle x\leq -\frac{31}{3}\)

Add three on both sides.

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

Simplify both sides.

\(\displaystyle -8x>12\)

Divide by negative eight on both sides.  Since we are dividing by a negative sign, the inequality sign will switch directions.

\(\displaystyle \frac{-8x}{-8}< \frac{12}{-8}\)

Reduce both fractions.

The answer is:  \(\displaystyle x< -\frac{3}{2}\)

In order to isolate the x-variable, first subtract five from both sides.

\(\displaystyle -6x+5-5>18-5\)

Simplify both sides.

\(\displaystyle -6x>13\)

Divide by negative six on both sides.  Remember to switch the sign since we are dividing by a negative number.

\(\displaystyle \frac{-6x}{-6}>\frac{13}{-6}\)

The answer is:  \(\displaystyle x< -\frac{13}{6}\)

Add \(\displaystyle 2x\) on both sides.

\(\displaystyle -2x+3+(2x)\geq 9x-7+(2x)\)

\(\displaystyle 3\geq11x-7\)

Add seven on both sides.

\(\displaystyle 3+(7)\geq11x-7+(7)\)

\(\displaystyle 10\geq11x\)

Divide by 11 on both sides.

\(\displaystyle \frac{10}{11}\geq \frac{11x}{11}\)

\(\displaystyle \frac{10}{11}\geq x\) OR \(\displaystyle x\leq \frac{10}{11}\)

The answer is:  \(\displaystyle x\leq \frac{10}{11}\)

To solve the inequality, isolate the integers on one side of the inequality, and the x-variables on another side.

To avoid having to divide by a negative coefficient of \(\displaystyle x\), subtract \(\displaystyle x\) on both sides.

\(\displaystyle x-3-(x)>6x-4-(x)\)

\(\displaystyle -3>5x-4\)

Add four on both sides.

\(\displaystyle -3+4>5x-4+4\)

Simplify both sides.

\(\displaystyle 1>5x\)

Divide by 5 on both sides.

\(\displaystyle \frac{1}{5}>\frac{5x}{5}\)

\(\displaystyle \frac{1}{5}>x\)

The answer is:  \(\displaystyle x< \frac{1}{5}\)

Add nine on both sides.

\(\displaystyle 8x-9+9>72+9\)

Simplify both sides.

\(\displaystyle 8x>81\)

Divide by eight on both sides.  There is no need to switch the sign.

\(\displaystyle \frac{8x}{8}>\frac{81}{8}\)

The answer is:  \(\displaystyle x>\frac{81}{8}\)

Isolate the x-variable terms on one side and the integers on the other.

Add \(\displaystyle 6x\) on both sides of the inequality.

\(\displaystyle -3x+6+(6x)< -6x+7+(6x)\)

\(\displaystyle 3x+6< 7\)

Subtract six from both sides.

\(\displaystyle 3x+6-6< 7-6\)

\(\displaystyle 3x< 1\)

Divide by three on both sides and simplify.

The answer is:  \(\displaystyle x< \frac{1}{3}\)

In order to isolate the \(\displaystyle x\) variable, subtract \(\displaystyle 6x\) from both sides.  This will prevent us from dividing a negative coefficient and change the sign.

\(\displaystyle 6x-3-6x\leq 9x+6-6x\)

Simplify both sides.

\(\displaystyle -3\leq 3x+6\)

Subtract six on both sides.

\(\displaystyle -3-6\leq 3x+6-6\)

Simplify both sides.

\(\displaystyle -9\leq 3x\)

Divide by three on both sides.

\(\displaystyle \frac{-9}{3}\leq\frac{ 3x}{3}\)

Simplify both sides.

The answer is:  \(\displaystyle x\geq-3\)