Exploring Compound Inequalities in Algebra

What are the two inequalities given in the problem?

• 3y + 7 = 2y and 4y + 8 = -48

• 3y + 7 < 2y and 4y + 8 < -48

• 3y + 7 > 2y and 4y + 8 < -48

• 3y + 7 < 2y and 4y + 8 > -48

What is the first step to isolate y in the inequality 3y + 7 < 2y?

• Add 7 to both sides

• Subtract 2y from both sides

• Add 2y to both sides

• Subtract 7 from both sides

After isolating y in the inequality 3y + 7 < 2y, what is the resulting inequality?

• y < 7

• y > -7

• y < -7

• y > 7

What is the first step to isolate y in the inequality 4y + 8 > -48?

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 8 from both sides

• Add 8 to both sides

After isolating y in the inequality 4y + 8 > -48, what is the resulting inequality?

• y > -14

• y < -14

• y > 14

• y < 14

What is the combined solution of the inequalities y < -7 and y > -14?

• -14 < y < -7

• y > -14 or y < -7

• -7 < y < -14

• y < -14 or y > -7

On a number line, how would you represent the solution -14 < y < -7?

• Closed circle on -14, open circle on -7, shading in between

• Open circles on -14 and -7, shading in between

• Closed circles on -14 and -7, shading in between

• Open circle on -14, closed circle on -7, shading in between

Which value satisfies both inequalities y < -7 and y > -14?

• 7

• 0

• -10

• -15

Why does the value 0 not satisfy the inequalities?

• 0 is not greater than -14

• 0 is not less than -7

• 0 is less than -14

• 0 is greater than -7

Why does the value -15 not satisfy the inequalities?

• -15 is not greater than -14

• -15 is not less than -7

• -15 is less than -14

• -15 is greater than -7