Algebra II : Setting Up Inequalities

Example Questions

Example Question #2056 : Algebra Ii

Set up the inequality:  The value of two less than eight times a number is between one and two.

Explanation:

Separate the parts of the sentence.

Two less than eight times a number:

If a quantity is between one and two, then the quantity cannot be one or two, and we will need to use less than signs.

Example Question #2057 : Algebra Ii

Set up the inequality:  Seven less than twice a number exceeds eleven.

Explanation:

Break up the statement into parts.

Twice a number:

Seven less than twice a number:

Exceeds eleven cannot be 11:

Combine the parts to form the inequality.

Example Question #2058 : Algebra Ii

Set up the inequality:  Four less than three times a number cannot exceed five.

Explanation:

Split the statement into parts.

Three times a number:

Four less than three times a number:

Cannot exceed five:

Cannot exceed five means that it can be five, but no more than five.

Combine the parts to form the inequality.

Example Question #2059 : Algebra Ii

Set up the inequality:   Five less than four times a number squared is at most seven.

Explanation:

Break up the sentence into parts.

A number squared:

Four times a number squared:

Five less than four times a number squared:

Is at most seven:

Combine the parts.

Example Question #2060 : Algebra Ii

Write the inequality:  The quantity of seven less than twice a number squared is no more than eleven.

Explanation:

Seven less than twice a number:

Square the quantity:

Is no more than eleven:

Combine the parts to form the inequality.

Example Question #21 : Inequalities

Set up the inequality:  Eight less than two-fifths of a number must exceed seven.

Explanation:

Break up the statement into parts.

Two-fifths of a number:

Eight less than two-fifths of a number:

Must exceed seven:

Example Question #221 : Basic Single Variable Algebra

Set up the inequality:  Five less than the squared quantity of three less a number must be more than eight.

Explanation:

Evaluate the inner quantity first.

Three less a number:

The squared quantity of three less a number:

Five less than the squared quantity of three less a number:

Must be more than eight:

Combine the parts to set up the inequality.

Example Question #222 : Basic Single Variable Algebra

Set up the inequality:  Eight less than seven times a number squared is at most four.

Explanation:

Break up the sentence into parts.

A number squared:

Seven times a number squared:

Eight less than seven times a number squared:

Is at most four:

Combine the parts to form the inequality.

Example Question #223 : Basic Single Variable Algebra

Set up the inequality:  Ten less than twice a number squared exceeds five.

Explanation:

Break up the inequality into parts.

Twice a number squared:

Ten less than twice a number squared:

Exceeds five:

Example Question #224 : Basic Single Variable Algebra

Set up the inequality:

Four times the quantity of seven less than three times a number cannot exceed eight.

Explanation:

Break up the sentence into parts.

Three times a number:

Seven less than three times a number:

Four times the quantity of seven less than three times a number:

Cannot exceed eight:

Combine the parts to form the inequality.