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 such as addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in a multistep inequality?

Back

To isolate a variable in a multistep inequality, perform inverse operations on both sides of the inequality, maintaining the inequality's direction unless multiplying or dividing by a negative number.

Front

What is the difference between solving an equation and solving an inequality?

Back

When solving an equation, the goal is to find a specific value for the variable. In contrast, solving an inequality results in a range of values that satisfy the inequality.

Front

What does it mean to reverse the inequality sign?

Back

The inequality sign is reversed when both sides of the inequality are multiplied or divided by a negative number.

Front

How can you check the solution of a multistep inequality?

Back

To check the solution of a multistep inequality, substitute a value from the solution set back into the original inequality to see if it holds true.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality is shown on a number line, where the solution set is indicated by an open or closed circle and a shaded region.

Front

What is the significance of the boundary point in an inequality?

Back

The boundary point in an inequality is the value that separates the solution set from the non-solution set; it is included in the solution if the inequality is 'less than or equal to' or 'greater than or equal to'.

Front

How do you solve the inequality 7(x + 3) < 5x + 13?

Back

Distribute 7 to get 7x + 21 < 5x + 13, then subtract 5x from both sides to get 2x + 21 < 13, and finally subtract 21 from both sides to find x < -4.

Front

What is the inequality that models a taxi fare of $2.50 per mile plus a $5 fee, not exceeding $20?

Back

The inequality is 2.50x + 5 ≤ 20, where x represents the number of miles.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

First, distribute -6 to get -3 - 24x - 36 > -111. Combine like terms to get -24x - 39 > -111, then add 39 to both sides to find -24x > -72, and finally divide by -24 to get x < 3.