Solving Linear Equations with Variables on Both Sides

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

• Combine like terms

• Divide both sides by the coefficient of the variable

• Move variables to one side to keep coefficients positive

• Add constants to both sides

How can you keep the variable's coefficient positive while solving?

• By moving the variable with a larger coefficient

• By moving the variable with a smaller coefficient

• By adding the variable to both sides

• By subtracting the variable from both sides

Why is it important to check the solution in equations with variables on both sides?

• To find alternative solutions

• To ensure the equation is balanced

• To determine if the equation is an identity

• To confirm the solution satisfies the original equation

What is the purpose of distributing before combining like terms?

• To simplify the equation for easier solving

• To prepare the equation for checking

• To isolate the variable immediately

• To find the variable's coefficient

What does it mean when an equation is called an identity?

• The equation simplifies to a contradiction

• The equation has no solutions

• The equation has exactly one solution

• The equation has infinitely many solutions

What indicates that an equation is a contradiction?

• It has exactly one solution

• It can be solved by isolating the variable

• It simplifies to an untrue statement like 3=4

• It simplifies to a true statement like 4=4

What is the result of an equation that simplifies to a statement like 7=7?

• No solution

• Infinitely many solutions

• Exactly one solution

• A contradiction

What does it mean if after solving an equation, both variables cancel out and leave a true statement?

• The equation is unsolvable

• The equation has no solution

• The equation is a contradiction

• The equation is an identity

In the real-world problem, what does 'x' represent?

• The total number of bulbs each has initially

• The number of bulbs planted

• The rate of planting bulbs per hour

• The number of hours spent planting

After how many hours will Elizabeth and Rachel have planted the same number of bulbs?

• 5 hours

• 4 hours

• 3 hours

• 2 hours