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

First subtract 2p from both sides:

p + 5 < 12.

Then subtract 5 from both sides:

p < 7

Since the inequality includes absolute value, you have two possiblities to consider: when the outcome is positive and when it is negative. When you consider the negative outcome, you must flip the inequality sign to solve for :

This means that is less than positive 20 AND greater than negative 20:

AND

For each case, you will first subtract 4 from the left to the right. Then, you will divide both sides by 4 to isolate :

AND

AND

This gives you the interval for valid values of :

First combine like terms on the right side of the inequality to obtain . Next, try to isolate the variable:.

The answer is therefore .

Distribute the negative sign first: becomes . Since there are no like-terms to combine on one side of the inequality sign, we will try to isolate the variable: . The answer is therefore .

Isolate the term with on one side and the constants on the other side.

First subtract 7x on both sides and add 5 to both sides.

Next, divide by 3 to solve for x.

To solve for the variable we need to isolate the variable on one side of the inequality and all other constants on the other side. In order to do this, perform inverse operations.

First subtracting 7 from both sides we get:

Then subtracting 2x from both sides:

Finally divide both sides by 2:

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by adding six to each side.

Whatever you do to one side you must also do to the other side.

This gives you:

The answer, therefore, is .

In order to isolate the variable, we will need to subtract 10 on both sides of the equation.

Simplify the left and the right side of the equation.

The answer is:

When you are solving for an inequality, it is easiest to treat the inequality sign as an equal sign while you solve for x.

In order to solve for x, you need to get x by itself on one side. The first thing you would need to do is subtract 6 from both sides. That would leave you with . In order to get x by itself, you need to divide both sides by 9. This would bring you to the answer of .

In order to isolate the variable, we need to move the 18 to the left side by subtracting 18 on both sides.

Simplify both sides.

This indicates that must be less than or equal to negative nine.

Rewrite the inequality so that the is on the left side, and the number is on the right side.

The answer is:

In order to isolate the x-variable, simply subtract 13 from both sides of the inequality.

Simplify both sides of the inequality.

There is no need to switch the sign.

The answer is:

In order to solve this inequality, we will need to subtract 30 from both sides of the equation.

Simplify both sides of the equation.

The answer is:

Solve by subtracting 13 on both sides of the inequality.

Simplify both sides. When subtracting a number from a negative number, the number will be increasingly negative.

The answer is:

To solve this inequality, we will need to group the variables on one side, and the constants on the other.

Subtract on both sides to move it to the right side.

Simplify both sides.

Subtract 18 from both sides.

Simplify both sides.

Divide by three on both sides.

Reduce the fractions.

The answer is:

Simplify the right side of the inequality.

Subtract nine on both sides.

Simplify both sides of the inequality.

The answer is:

In order to isolate the variable, subtract 7 from both sides of the inequality.

Simplify both sides.

The answer is:

Group the integers on the left side and the values on the right side.

Subtract three on both sides.

Simplify both sides.

Subtract on both sides.

Simplify both sides.

The answer is:

Solve this inequality by subtracting six from both sides. This will isolate the x-variable.

Simplify both sides. A negative number subtracting a number will be further way from zero.

The answer is:

Subtract nine on both sides.

Simplify both sides.

The answer is: