Distributing Negatives and Inequalities

The video tutorial explains how to solve a linear inequality by distributing negative values, combining like terms, and isolating variables. It demonstrates the importance of reversing the inequality when dividing by a negative number. The solution is represented graphically on a number line and expressed in interval notation.

What is the first step in solving the given linear inequality?

• Reversing the inequality

• Combining like terms

• Distributing negative seven

• Adding 7 to both sides

What is the inequality that results from distributing negative seven?

• -7x - 7 + 3x < 15

• -7x + 7 + 3x < 15

• 7x - 7 + 3x < 15

• 7x + 7 + 3x < 15

When distributing a negative one, what happens to the signs of the terms?

• They remain the same

• They become positive

• They change to the opposite sign

• They double in value

What is the result of distributing negative one across the binomial?

• -x - 1

• x + 1

• -x + 1

• x - 1

After distributing, what is the result of combining -7x and 3x?

• -10x

• 10x

• -4x

• 4x

What is the simplified form of the inequality after combining like terms?

• -4x > 14

• 4x < 14

• 4x > 14

• -4x < 14

What operation is performed to isolate the variable on one side of the inequality?

• Dividing by 3

• Multiplying by 3

• Adding 7

• Subtracting 7

What is the next step after isolating the variable on one side?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply by 3

• Divide by 3

What must you remember to do when dividing both sides of an inequality by a negative number?

• Add 1 to both sides

• Subtract 1 from both sides

• Reverse the inequality sign

• Keep the inequality sign the same

What is the final inequality after reversing the inequality sign?

• x >= -7

• x > -7

• x < -7

• x <= -7