Solving Linear Equations and Inequalities

The video tutorial covers solving equations with variables on both sides, isolating variables, handling fractions, understanding reflexive properties, and dealing with equations that have infinite or no solutions. It also includes practical examples like solving for equal perimeters and eliminating fractions to simplify equations.

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

• Add the same number to both sides

• Subtract the same number from both sides

• Isolate the variable on one side

• Multiply both sides by the same number

In the equation 7x = 3x + 2, what should you do first to solve for x?

• Add 3x to both sides

• Subtract 3x from both sides

• Subtract 2 from both sides

• Add 2 to both sides

What is the result of isolating the variable in the equation 4x = 2?

• x = 1

• x = 2

• x = 1/2

• x = 4

When solving 5x + 7x = 12x, what is the next step after combining like terms?

• Divide both sides by 12

• Subtract 7x from both sides

• Add 5x to both sides

• Subtract 12x from both sides

What does it mean if an equation simplifies to 6x = 6x?

• x is undefined

• x is zero

• x can be any number

• x has no solution

If an equation results in 0 = 2, what does this indicate?

• The equation has a unique solution

• The equation has no solution

• The equation is undefined

• The equation is always true

How do you solve for x in the equation 2x + 8 = 2(2x + 1)?

• x = 4

• x = 3/2

• x = 1

• x = 2

What is the least common multiple of 6, 2, 4, and 3?

• 24

• 12

• 6

• 18

Why is it useful to multiply both sides of an equation by the least common multiple?

• To eliminate fractions

• To make the equation more complex

• To change the variable

• To increase the number of solutions