Exploring Two-Step Inequalities and Graphing

What is the first step in solving the inequality -30 ≥ -10 + 10x?

• Multiply both sides by 10

• Subtract 10 from both sides

• Add 10 to both sides

• Divide both sides by 10

What happens to the inequality symbol when the order of x and the number is flipped?

• It is inverted

• It remains the same

• It disappears

• It becomes an equation

On a number line, how is 'x ≤ -2' represented?

• Filled circle at -2, arrow pointing left

• Open circle at -2, arrow pointing left

• Filled circle at -2, arrow pointing right

• Open circle at -2, arrow pointing right

What does the inequality symbol change to when the sides are flipped?

• ≤ becomes ≥

• ≥ becomes ≤

• No change occurs

• Both A and B

What is the solution to the inequality x + 7 ≥ 2 after subtracting 7 from both sides?

• x ≤ 5

• x ≥ -5

• x ≤ -5

• x ≥ 5

How is the solution 'x ≥ -1' represented on a number line?

• Filled circle at -1, arrow pointing right

• Filled circle at -1, arrow pointing left

• Open circle at -1, arrow pointing left

• Open circle at -1, arrow pointing right

What does an open circle on a number line indicate?

• The solution is zero at this point

• The number is included in the solution

• The number is not included in the solution

• The solution is undefined at this point

If 5x - 4 > 46, what is the first step to isolate x?

• Subtract 5 from both sides

• Add 4 to both sides

• Divide both sides by 5

• Multiply both sides by 5

What is the correct representation for 'x > 10' on a number line?

• Filled circle at 10, arrow pointing right

• Open circle at 10, arrow pointing left

• Filled circle at 10, arrow pointing left

• Open circle at 10, arrow pointing right

What type of numbers can be solutions for 'x > 10'?

• Integers greater than 11

• Any number less than 10

• Only whole numbers greater than 10

• Any number greater than 10, including decimals