To solve for $\displaystyle x$, separate the integers and $\displaystyle x$'s by adding 1 and subtracting $\displaystyle x$ from both sides to get $\displaystyle 2x>8$. Then, divide both sides by 2 to get $\displaystyle x>4$. Since you didn't divide by a negative number, the sign does not need to be reversed.

$\displaystyle -2x+3-3>4-3$

$\displaystyle -2x>1$

$\displaystyle \frac{-2x}{-2}< \frac{1}{-2}$    Don't forget to change the direction of the inequality sign when dividing by a negative number!

$\displaystyle x< -\frac{1}{2}$

$\displaystyle -4x + 17 > 81$

$\displaystyle -4x + 17 -17 > 81 -17$

$\displaystyle -4x > 64$

$\displaystyle -4x \div (-4)< 64 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$\displaystyle x < -16$

or, in interval form,

$\displaystyle (-\infty ,-16)$

$\displaystyle -5x + 17 \geq 82$

$\displaystyle -5x + 17 -17 \geq 82-17$

$\displaystyle -5x \geq 65$

$\displaystyle -5x \div (-5) \leq 65\div (-5)$ 

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$\displaystyle x \leq -13$ 

or, in interval form,

$\displaystyle (-\infty , -13]$

$\displaystyle -5x + 27 \leq 62$

$\displaystyle -5x + 27 -27 \leq 62-27$

$\displaystyle -5x \leq 35$

$\displaystyle -5x \div (-5) \leq 35\div (-5)$ 

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$\displaystyle x \geq -7$ 

or, in interval form,

$\displaystyle [-7,\infty )$

$\displaystyle -4x - 11 < 57$

$\displaystyle -4x - 11 + 11 < 57 + 11$

$\displaystyle -4x < 68$

$\displaystyle -4x \div (-4) > 68 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$\displaystyle x > -17$

or, in interval form,

$\displaystyle (-17,\infty )$

$\displaystyle -4x + 11 < 67$

$\displaystyle -4x + 11 - 11 < 67- 11$

$\displaystyle -4x < 56$

$\displaystyle -4x \div (-4) > 56 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$\displaystyle x > -14$

or, in interval form,

$\displaystyle (-14, \infty )$

First, add $\displaystyle 2x$ and subtract $\displaystyle 2$ from both sides of the inequality to get $\displaystyle -4x>8$.

Then, divide both sides by $\displaystyle -4$ and reverse the sign since you are dividing by a negative number.

This gives you $\displaystyle x< -2$.

Solve each of these two inequalities separately:

$\displaystyle 4y + 15 < 91$

$\displaystyle 4y + 15 - 15 < 91- 15$

$\displaystyle 4y < 76$

$\displaystyle 4y \div 4 < 76 \div 4$

$\displaystyle y < 19$, or, in interval form, $\displaystyle (-\infty , 19)$

$\displaystyle 7y -12 > 86$

$\displaystyle 7y -12 + 12 > 86 + 12$

$\displaystyle 7y > 98$

$\displaystyle 7y \div 7 > 98 \div 7$

$\displaystyle y > 14$, or, in interval form, $\displaystyle (14, \infty )$

The two inequalities are connected with an "and", so we take the intersection of the two intervals.

$\displaystyle (14, \infty ) \cap (-\infty , 19) = (14,19)$

$\displaystyle 0.4 x - 1.7 \geq -8.5$

$\displaystyle 0.4 x - 1.7 + 1.7 \geq -8.5+ 1.7$

$\displaystyle 0.4 x \geq -6.8$

$\displaystyle 0.4 x \div 0.4 \geq -6.8\div 0.4$

$\displaystyle x \geq -17$

or, in interval form, $\displaystyle [-17, \infty )$