Solving Equations and Inequalities

Mrs. Lopez introduces solving linear equations, emphasizing the importance of reviewing two-step equations from grade 7. She provides examples of solving equations with variables on both sides and multiple-step equations. The lesson concludes with a review of solutions and homework instructions.

Why is it important to review two-step equations from grade seven before tackling more complex equations in grade eight?

• They provide a foundation for understanding more complex equations.

• They are only used in grade seven exams.

• Because they are easier to solve.

• They are not relevant to grade eight material.

What is the first step in solving the equation 4 + 15x = 49?

• Add 4 to both sides.

• Divide both sides by 15.

• Multiply both sides by 15.

• Subtract 4 from both sides.

When solving an equation with variables on both sides, what is the primary goal?

• To add the same number to both sides.

• To multiply both sides by zero.

• To isolate the variable on one side.

• To eliminate all constants.

How do you handle fractions when solving equations?

• Ignore them.

• Convert them to decimals.

• Use the reciprocal to eliminate them.

• Add them to both sides.

What is the reciprocal of 3/5?

• 1/5

• 1/3

• 3/5

• 5/3

In the equation 3/5x + (-21) = 15, what is the first step to isolate x?

• Subtract 21 from both sides.

• Multiply by 5/3.

• Add 21 to both sides.

• Divide by 3/5.

What is the result of simplifying 1/5x + x?

• 6/5x

• 5/5x

• 1/5x

• 1x

What is the solution to the equation 10 and 1/5x = 10?

• x = 5

• x = 1

• x = 10

• x = 51/50

What is the first step in checking your solution to an equation?

• Substituting the solution back into the original equation.

• Multiplying both sides by zero.

• Adding a random number to both sides.

• Rewriting the equation.

What is the purpose of using the distributive property in solving equations?

• To add more terms to the equation.

• To make the equation longer.

• To simplify the equation by distributing multiplication over addition.

• To eliminate all variables.