# Algebra 1 : Systems of Inequalities

## Example Questions

### Example Question #11 : Equations / Inequalities

Solve the following inequality:

Explanation:

In order to isolate  variable, multiply by four on both sides of the equation.

Simplify both sides of the inequality.

### Example Question #12 : Equations / Inequalities

Solve:

Explanation:

Multiply by seven on both sides of the equation.  There is no need to change the direction of the sign unless there is a negative sign.

Simplify both sides.

### Example Question #11 : Systems Of Inequalities

Solve the inequality:

Explanation:

In order to isolate the unknown variable, we will need to multiply the reciprocal of the coefficient on both sides of the inequality sign.

Simplify both sides of the equation.

### Example Question #14 : Equations / Inequalities

Solve:

Explanation:

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

Simplify both sides.  The nine on the right side of the inequality can be split into factors.

### Example Question #15 : Equations / Inequalities

Solve the inequality and rewrite in interval notation:

Explanation:

In order to isolate the variable, we can multiply both sides by the reciprocal of the coefficient in front of the x variable.

Simplify both sides of the equation.

This indicates that the x-variable is four ninths or greater.  Use a bracket sign to indicate that it includes the fraction.  The infinity isn't finite, which means that a parenthesis should enclose this symbol instead of a bracket.

### Example Question #16 : Equations / Inequalities

Solve the inequality:

Explanation:

In order to isolate the x variable, we will need to divide by negative one sixth on both sides.  The result will switch the sign of the inequality.

This is also the same as multiplying by negative six on both sides.

Switch the sign.

Upon testing values that are less than negative 36, we will find that those values will satisfy the inequality instead of .

### Example Question #17 : Equations / Inequalities

Solve the following inequality:

Explanation:

In order to isolate the x-variable, we will need to multiply both sides by the reciprocal of the coefficient in front of the x.

Simplify both sides.  A whole number will multiply to the numerator of a fraction.

### Example Question #18 : Equations / Inequalities

Solve:

Explanation:

To isolate the x-variable, we will need to multiply by eight on both sides.

Simplify both sides of the equation.

### Example Question #19 : Equations / Inequalities

Find the solution to the inequality:

Explanation:

In order to isolate the x-variable, we will need to multiply by nine on both sides of the inequality.

Simplify both sides of the equation.

Reduce the fraction on the right side.

### Example Question #20 : Equations / Inequalities

Solve the inequality: