How to find the solution to an inequality with division - Algebra 1

To solve this inequality, get the 's to one side of the equation and the integers to the other side.

Add 1 to both sides:

Divide both sides by 2:

(Since we are not dividing by a negative number, there is no need to reverse the sign.)

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

First, add and subtract from both sides of the inequality to get .

Then, divide both sides by and reverse the sign since you are dividing by a negative number.

This gives you .

Don't forget to change the direction of the inequality sign when dividing by a negative number!

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

or, in interval form,

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

or, in interval form,

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

or, in interval form,

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

or, in interval form,

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

or, in interval form,

Solve each of these two inequalities separately:

, or in interval form,

(Note the flipping of the inequality because of the division by a negative number.)

, or in interval form,

The question asks about the intersection of the two intervals:

The intersection is the area of the number line that the two sets share, or .

Solve each of these two inequalities separately:

, or, in interval form,

, or, in interval form,

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

Note the switch in inequality symbols when the numbers are divided by a negative number.

or, in interval form:

or, in interval form,

Solve each inequality separately:

or, in interval form,

or, in interval form,

Since these statements are connected by an "or", we are looking for the union of the intervals. Since the intervals are disjoint, we can simply write this as

To solve the inequality, you must first separate the integers and the 's. Subtract and add to both sides of the inequality to get

.

Then, divide both sides by to get

.

Since you are not dividing by a negative number, the sign does not need to be reversed.

First, use the distributive property to simplify the right side of the inequality:

.

Then, add and subtract from both sides of the inequality to get

.

Finally, divide from both sides to get .

To solve this inequality, move all the terms with on one side and all other terms on the other side, then solve for x.

Inequalities are treated as equalities when it comes to balancing, with the exception of division by a negative number (then flip the greater/less than symbol).

The question is asking for the solved inequality isolating . Combine like terms across sides by adding or subtracting same value to both sides.

Use the properties of inequalities to balance the inequality and isolate .

First subtract three from both sides.

Next, divide by four.

Since no division or multiplication of a negative number occurred, the inequality sign remains the same.