Solving Linear Equations

What does it mean to 'subtract the constant' in an equation?

• To add the constant to both sides of the equation.

• To remove the number that is not attached to a variable from both sides of the equation.

• To multiply both sides of the equation by the constant.

• To divide both sides of the equation by the constant.

What is the first step in solving the equation -12t + 10 + 32 = 78?

• Combine like terms: -12t + 42 = 78.

• Add 10 and 32 to both sides of the equation.

• Subtract 10 from both sides of the equation.

• Multiply both sides by -1.

What is the solution to the equation -12 = 10n - 40n + 3?

• n = 1/4 or 0.25

• n = 1/2 or 0.5

• n = 1 or 1.0

• n = 3/2 or 1.5

How do you solve for p in the equation 15 - 8p + 6.75p = 10?

• Combine like terms to get 15 - 1.25p = 10, then isolate p.

• Subtract 15 from both sides to get -8p + 6.75p = -5.

• Add 8p to both sides to get 6.75p = 15 - 10.

• Multiply both sides by -1 to get 8p - 6.75p = -15.

What is the difference between an equation and an expression?

• An equation is a statement that two expressions are equal, while an expression is a combination of numbers, variables, and operations without an equal sign.

• An equation is a mathematical statement that includes an equal sign, while an expression does not include any variables.

• An equation is a type of expression that always results in a number, while an expression can only contain variables.

• An equation is a combination of numbers and operations, while an expression is a statement that two equations are equal.

What is a linear equation?

• A linear equation is an equation that makes a straight line when graphed.

• A linear equation is a polynomial of degree two.

• A linear equation is an equation that represents a curve.

• A linear equation is an equation that has no solutions.

What is the solution to the equation 4x + 14 + 4x = 38?

• x = 1

• x = 2

• x = 3

• x = 4

What does 'combining like terms' mean?

• Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

• Combining like terms means to multiply different terms together to create a new term.

• Combining like terms means to separate terms that have different variables into distinct groups.

• Combining like terms means to rearrange the terms in an expression without changing their values.

How can you verify your answer after solving a linear equation?

• By checking the solution with a calculator.

• By substituting the solution back into the original equation to see if both sides are equal.

• By asking a friend if the answer seems correct.

• By rewriting the equation in a different form.

How do you isolate a variable in an equation?

• By adding the same value to both sides of the equation.

• By performing inverse operations to get the variable on one side of the equation and the constants on the other side.

• By multiplying both sides of the equation by the variable.

• By dividing both sides of the equation by the constant.