Solving Linear Equations and Inequalities

This lesson focuses on solving linear equations, starting with basic strategies like subtracting and multiplying both sides of an equation. Students engage in a card activity to practice solving equations and explore a number puzzle to deepen their understanding. The lesson concludes with a summary and homework solutions, emphasizing the importance of practice and different approaches to solving equations.

What is the first step in solving the equation -6x - 7 = 4x - 2 to make x positive?

• Subtract 4x from both sides

• Add 6x to both sides

• Add 7 to both sides

• Multiply both sides by -1

When solving the equation 12x + 7 = x + 13, what operation can be used to eliminate the fraction?

• Subtract x from both sides

• Divide everything by 2

• Add 7 to both sides

• Multiply everything by 2

In the equation 2(x + 7) = -4x + 14, what is the result after using the distributive property?

• 2x + 7 = -4x - 14

• 2x + 14 = -4x - 14

• 2x + 7 = -4x + 14

• 2x + 14 = -4x + 14

What is the correct way to solve for x in the equation 2x + 10 = 3x + 1?

• Subtract 2x from both sides

• Add 1 to both sides

• Add 10 to both sides

• Subtract 3x from both sides

What mistake did CLA make when distributing 12 in her equation?

• She multiplied 12 by 5 incorrectly

• She forgot to distribute to all terms

• She used the wrong sign for multiplication

• She added instead of subtracting

What is the correct solution for the equation 2m - 16 = 9/3 + 2m?

• m = 7

• m = -7

• m = 0

• m = 3

What is the result of combining like terms in the equation 60 + 24y = 4y - 5 + 9y?

• 60 + 24y = 13y

• 60 = 13y - 5

• 24y = 13y - 5

• 60 + 24y = 13y - 5

How can you verify the slope of a line is 1/4 using points on the graph?

• Ensure the line is horizontal

• Check if the line passes through the origin

• Verify the line is vertical

• Calculate the difference in y-values over x-values

What is the slope of a line if a participant walks 21 miles at 3 miles per hour?

• 0

• 3

• -3

• 21

What is the y-intercept of a line if it crosses the y-axis at a little over one?

• 1/4

• A little over one

• 1

• 0