Solving Linear Equations Concepts

Lesson 24 covers solving equations with variables on each side. The process involves moving all variables to one side and numbers to the other, then solving as usual. Examples include solving 5x + 2 = 6 - 7x, using the distributive property, and identifying equations with no solution or those true for all real numbers.

What is the first step in solving an equation with variables on both sides?

• Add numbers to both sides

• Divide both sides by the variable

• Multiply both sides by zero

• Add or subtract to get variables on one side

In the equation 5x + 2 = 6 - 7x, what operation is used to move the variable terms to one side?

• Add 5x to both sides

• Subtract 7x from both sides

• Add 7x to both sides

• Subtract 5x from both sides

After moving the variables in the equation 5x + 2 = 6 - 7x, what is the resulting equation?

• 12x = 4

• 12x + 2 = 6

• 5x = 6 - 7x

• 5x + 2 = 6

What is the solution to the equation 12x = 4?

• x = 1/3

• x = 1/4

• x = 4

• x = 3

What is the result of dividing both sides of the equation 12x = 4 by 12?

• x = 3

• x = 1/4

• x = 1/3

• x = 4

What property is used when solving equations with parentheses?

• Associative Property

• Commutative Property

• Distributive Property

• Identity Property

In the equation 8(5x - 2) = 10(32 + 4x), what happens when you distribute the terms?

• 40x - 16 = 320 + 40x

• 40x + 16 = 320 + 40x

• 40x - 16 = 320 - 40x

• 40x + 16 = 320 - 40x

What is the solution to the equation 40x - 16 = 320 + 40x?

• No solution

• x = 1

• All real numbers

• x = 0

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

• To eliminate fractions

• To simplify equations with parentheses

• To add variables

• To subtract numbers

In the equation 4(x + 20) = 1/5(20x + 400), what is the result after distributing?

• 4x + 80 = 80x + 4

• 4x + 80 = 4x + 80

• 4x + 80 = 80x + 20

• 4x + 20 = 4x + 80