Solving 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 operations like addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does '≥' signify in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either greater than or equal to the value on the right side.

Front

What does '≤' signify in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either less than or equal to the value on the right side.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the line in the direction of the inequality.

Front

What is the first step in solving the inequality 12x + 400 < 1200?

Back

The first step is to subtract 400 from both sides of the inequality, resulting in 12x < 800.

Front

What is the solution to the inequality 12x < 800?

Back

To solve for x, divide both sides by 12, resulting in x < 66.67.

Front

What is the solution to the inequality -3 - 6(4x + 6) > -111?

Back

First, simplify to get -3 - 24x - 36 > -111, then combine like terms to find -24x > -72, and finally divide by -24, reversing the inequality to get x < 3.