Solving Inequalities with Negative Coefficients

Why is it often easier to work with positive coefficients in inequalities?

• Negative coefficients are not allowed in inequalities.

• Positive coefficients simplify the arithmetic.

• Positive coefficients make the inequality true.

• Positive coefficients are always larger.

What is the first step in solving the inequality -5x + 7 ≥ 12?

• Multiply by 5.

• Divide by -5.

• Subtract 7 from both sides.

• Add 5x to both sides.

After subtracting 7 from both sides in the inequality -5x + 7 ≥ 12, what is the resulting inequality?

• 5x ≤ 5

• 5x ≥ 5

• -5x ≤ 5

• -5x ≥ 5

What do you get when you add 5x to both sides of the inequality -5x + 7 ≥ 12?

• 0 ≤ 5 + 5x

• 0 ≥ 5 + 5x

• 5x ≤ 5

• 5x ≥ 5

How do you rewrite the inequality -1 ≥ x?

• x ≥ -1

• x < -1

• x ≤ -1

• x > -1

What is the purpose of graphing the inequality x ≤ -1?

• To check if the inequality is correct.

• To visually represent the solution set.

• To find the exact value of x.

• To compare it with other inequalities.

What is the first step in solving the inequality 10 - 3x > 37?

• Divide by 3.

• Subtract 37 from both sides.

• Add 3x to both sides.

• Subtract 10 from both sides.

After adding 3x to both sides in the inequality 10 - 3x > 37, what is the resulting inequality?

• 10 ≤ 37 + 3x

• 10 > 37 + 3x

• 10 < 37 + 3x

• 10 ≥ 37 + 3x

What do you get when you subtract 37 from both sides of the inequality 10 > 37 + 3x?

• 27 > 3x

• -27 < 3x

• -27 > 3x

• 27 < 3x

How do you rewrite the inequality -9 > x?

• x ≥ -9

• x < -9

• x ≤ -9

• x > -9