Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 18 ≥ 5k + 4k?

Back

Combine like terms to get 18 ≥ 9k, then divide both sides by 9 to find k ≤ 2.

Front

What is the solution set for the inequality 6 - 2h > 30?

Back

First, subtract 6 from both sides to get -2h > 24, then divide by -2 (remember to flip the inequality) to find h < -12.

Front

What does the inequality -4x + 14 ≤ 54 represent?

Back

It represents a range of values for x that satisfy the condition when simplified to x ≥ -10.

Front

How do you isolate the variable in the inequality a - 6 ≤ 15 + 8a?

Back

Add 6 to both sides to get a ≤ 21 + 8a, then subtract 8a from both sides to find -7a ≤ 21, leading to a ≥ -3.

Front

What is the first step in solving the inequality 3x + 5 < 20?

Back

Subtract 5 from both sides to simplify the inequality to 3x < 15.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality, often resulting in a contradiction.

Front

How do you graph the solution of the inequality x > 4?

Back

Draw a number line, place an open circle on 4, and shade to the right to indicate all numbers greater than 4.

Front

What is the difference between < and ≤ in inequalities?

Back

< means 'less than' and does not include the endpoint, while ≤ means 'less than or equal to' and includes the endpoint.

Front

How do you check if a number is in the solution set of an inequality?

Back

Substitute the number into the original inequality and see if the statement is true.