Solving Equations and Inequalities with Variables on Both Sides

What is a common mistake students make when solving equations with variables on both sides?

• Multiplying both sides by the same number

• Adding constants to both sides

• Dividing both sides by the same number

• Combining variables on both sides directly

When solving an equation with variables on both sides, what operation should be used to move a term to the other side?

• Inverse operations

• Division

• Multiplication

• Direct addition

In the example provided, what is the result of distributing 3 through the parentheses on the left side?

• 12x + 3

• 3x + 4

• 6x + 12

• 9x + 12

After distributing and combining like terms, what is the next step to isolate the variable x?

• Add the constants on both sides

• Subtract the smaller variable term from both sides

• Multiply both sides by the same number

• Divide both sides by the same number

What is the main difference between solving equations and inequalities?

• The process is different

• The symbols used are different

• Inequalities require more steps

• Equations are easier to solve

How is the solution represented on a number line for an inequality?

• With a shaded region

• With a closed circle

• With an open circle

• With a dashed line

What does 'no solution' mean in the context of solving equations?

• The equation has no variables

• The equation has no constants

• No value for the variable can satisfy the equation

• The equation has infinite solutions

What is the symbol for 'no solution'?

• A blank space

• An infinity symbol

• A zero with a slash through it

• A question mark

What does 'all real numbers' or 'infinitely many solutions' mean?

• The equation has no solution

• The equation has one solution

• Every value for the variable satisfies the equation

• The equation has a finite number of solutions

How is 'all real numbers' represented on a number line?

• With a single point

• With a shaded region

• With the entire number line shaded

• With a dashed line