Linear Equations and Solutions

This lesson introduces linear equations in X, defining them and exploring their truth values. It explains how to solve linear equations by finding values of X that satisfy the equation. The lesson includes examples of linear equations and discusses different types of equations, such as two-step equations and those involving the distributive property. The video concludes with a variety of examples to reinforce understanding.

What is a linear equation in X?

• An equation with multiple variables.

• An equation with no variables.

• An equation where two linear expressions are equal.

• An equation with a variable raised to the power of two.

How can you determine if a linear equation is true?

• By checking if both sides are negative.

• By ensuring both sides have the same number of terms.

• By verifying that both sides are positive.

• By checking if the left side equals the right side.

What is the solution to a linear equation?

• A number that makes the equation true.

• A number that makes both sides negative.

• A number that makes the equation false.

• A number that makes both sides positive.

If 4 + 15x = 49, is x = 2 a solution?

• Yes, because 49 equals 49.

• No, because 49 does not equal 49.

• No, because 34 does not equal 49.

• Yes, because 34 equals 49.

Is x = 3 a solution for the equation 4 + 15x = 49?

• Yes, because 49 equals 49.

• No, because 49 does not equal 49.

• Yes, because 34 equals 49.

• No, because 34 does not equal 49.

For the equation 8x - 19 = -4 - 7x, is x = 5 a solution?

• No, because 21 does not equal 21.

• Yes, because 21 equals -39.

• No, because 21 does not equal -39.

• Yes, because 21 equals 21.

Is x = 6 a solution for the equation -2x + 11 - 5x = 5 - 6x?

• No, because -31 does not equal 31.

• No, because -31 does not equal -31.

• Yes, because -31 equals 31.

• Yes, because -31 equals -31.

What is a two-step equation?

• An equation with two equal signs.

• An equation with two solutions.

• An equation with two variables.

• An equation that requires two operations to solve.

What does the distributive property involve?

• Subtracting terms on both sides.

• Dividing terms on both sides.

• Multiplying a single term across terms inside parentheses.

• Adding terms on both sides.

What does it mean to have variables on both sides of an equation?

• The equation has only one variable.

• The equation has variables on both sides of the equal sign.

• The equation has no solution.

• The equation is unsolvable.