Solving Inequalities

Front

What does the inequality symbol '<' indicate about a value?

Back

It indicates that the solution is less than a value.

Front

How do you solve the inequality \( \frac{d}{2} - 1 \ge 3 \)?

Back

Add 1 to both sides to get \( \frac{d}{2} \ge 4 \), then multiply both sides by 2 to find \( d \ge 8 \).

Front

What is the solution to the inequality \( 4k + 15 > -2k + 3 \)?

Back

Combine like terms to get \( 6k > -12 \), then divide by 6 to find \( k > -2 \).

Front

How can you represent the inequality shown on a number line where the graph starts at 0 and includes all values to the right?

Back

The inequality is represented as \( x \ge 0 \).

Front

What is the first step to solve the inequality \( -6(w + 1) < 2(w + 5) \)?

Back

Distribute both sides: \( -6w - 6 < 2w + 10 \).

Front

What does the inequality symbol '>' signify in a mathematical context?

Back

It signifies that the solution is greater than a value.

Front

When solving inequalities, what is the effect of multiplying or dividing by a negative number?

Back

It reverses the direction of the inequality sign.

Front

What is the solution to the inequality \( 2x - 3 < 5 \)?

Back

Add 3 to both sides to get \( 2x < 8 \), then divide by 2 to find \( x < 4 \).

Front

How do you graph the solution to the inequality \( x < 3 \)?

Back

Draw a number line, place an open circle at 3, and shade to the left.

Front

What is the solution to the inequality \( 3y + 4 \, \leq \, 10 \)?

Back

Subtract 4 from both sides to get \( 3y \leq 6 \), then divide by 3 to find \( y \, \leq \, 2 \).