2 step inequalities

Front

What is a 2-step inequality?

Back

An inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (flip the inequality sign): x ≥ -10.

Front

When do you use a closed circle on a graph for an inequality?

Back

When it is ≥ or ≤.

Front

What does the inequality x < 6 represent on a number line?

Back

All numbers less than 6, represented with an open circle at 6.

Front

When do you 'flip the inequality sign'?

Back

When you multiply or divide both sides of the inequality by a negative number.

Front

Solve and graph the inequality: 7n - 1 > 76.

Back

1. Add 1 to both sides: 7n > 77. 2. Divide by 7: n > 11. Graph: open circle at 11, shading to the right.

Front

What is the solution set for the inequality x + 5 < 12?

Back

x < 7.

Front

How do you represent the solution of x ≥ 3 on a number line?

Back

Closed circle at 3, shading to the right.

Front

What is the difference between < and ≤ in inequalities?

Back

< means 'less than' (open circle), while ≤ means 'less than or equal to' (closed circle).

Front

What does the inequality -2x + 3 > 1 mean?

Back

1. Subtract 3: -2x > -2. 2. Divide by -2 (flip the sign): x < 1.