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 solve the inequality 6(n + 2) < -72?

Back

First, distribute: 6n + 12 < -72. Then, subtract 12 from both sides: 6n < -84. Finally, divide by 6: n < -14.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to another value.

Front

How do you check if a value satisfies the inequality x + 9 > 21 when x = 15?

Back

Substitute 15 into the inequality: 15 + 9 > 21. This simplifies to 24 > 21, which is true.

Front

What is the solution to the inequality -138 ≥ -6(6b - 7)?

Back

First, distribute: -138 ≥ -36b + 42. Then, subtract 42 from both sides: -180 ≥ -36b. Finally, divide by -36 (remember to flip the inequality): b ≥ 5.

Front

What is the first step in solving the inequality m - (-3) > 17?

Back

The first step is to simplify: m + 3 > 17.

Front

What is the solution to the inequality m + 3 > 17?

Back

Subtract 3 from both sides: m > 14.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, often resulting from contradictory statements.

Front

What is the difference between '>' and '<' in inequalities?

Back

'>' means 'greater than', while '<' means 'less than'. They indicate the direction of the inequality.

Front

How do you represent the solution of an inequality on a number line?

Back

Use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the direction of the solution.