Algebra 1 : Systems of Inequalities

Example Questions

Example Question #2142 : Algebra 1

Solve:

Explanation:

To isolate the x variable, multiply the reciprocal of the fraction in front of the variable on both sides of the inequality.

Simplify both sides of the inequality.

Example Question #21 : Systems Of Inequalities

Solve the following inequality:

Explanation:

In order to eliminate the fractions, multiply the inequality by three on both sides.

This will make the inequality easier to solve.

Distribute and simplify both sides.

Subtract two from both sides.

Example Question #23 : Equations / Inequalities

Solve the inequality:

Explanation:

Multiply both sides by three halves.

Simplify both sides.  Multiply the integer with the numerator on the right side of the inequality.

Example Question #21 : Systems Of Inequalities

Solve the following inequality:

Explanation:

Solve this inequality by multiplying both sides by the reciprocal of the coefficient in front of the x-variable.

Simplify both sides.  Multiply the integer by the numerator on the right side of the inequality.

Example Question #22 : Systems Of Inequalities

Solve the following inequality:

Explanation:

Multiply the reciprocal of the fraction in front of the  variable on both sides of the equation.

Simplify both sides.

Reduce the fraction on the right side.

Example Question #26 : Equations / Inequalities

Solve the inequality:

Explanation:

Multiply both sides by the reciprocal of the fraction in front of the x-variable.

Simplify both sides.  There is no need to switch the sign.  Multiply the negative integer with the numerator on the right side of the inequality.

Example Question #23 : Systems Of Inequalities

Solve the inequality:

Explanation:

In order to isolate the x-variable, we will need to divide both sides by nine.  To avoid writing a complex fraction on the right side, dividing by nine is similar to multiplying by one-ninth.

Multiply by one-ninth on both sides.

Simplify both sides.  Multiply the denominator with denominator on the right side.  Since we have divide by a positive number on both sides, there is no need to switch the sign.

Example Question #24 : Systems Of Inequalities

Solve the inequality:

Explanation:

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

Example Question #25 : Systems Of Inequalities

Solve the inequality:

Explanation:

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

Example Question #3 : How To Find The Solution To An Inequality With Subtraction

Which one of the following is is a valid value for ?

Explanation:

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 :