Multi-step Equations

What is a multi-step equation?

• An equation that can be solved in one step.

• An equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

• An equation that has no solution.

• An equation that only involves addition and subtraction.

What is the goal when solving multi-step equations?

• To isolate the variable on one side of the equation to find its value.

• To simplify the equation by combining like terms only.

• To eliminate all constants from the equation.

• To find the greatest common factor of the coefficients.

What is an identity in equations?

• An identity is an equation that is true for all values of the variable, such as 2x + 3 = 2x + 3.

• An identity is an equation that has no solutions.

• An identity is an equation that is true for some values of the variable.

• An identity is a type of inequality that compares two expressions.

Solve the equation: 4x + 10 = -26

• x = -5

• x = -7

• x = -9

• x = -11

What does it mean if an equation has no solution?

• An equation has no solution when there are no values that can satisfy the equation, often resulting in a contradiction.

• An equation has no solution when it can be simplified to a single variable.

• An equation has no solution when it has infinitely many solutions.

• An equation has no solution when it is always true regardless of the variable.

Which equation has no solution: 2x + 1 = 5x - 3 or 3(2x + 1) = 6x + 1?

• 2x + 1 = 5x - 3

• 3(2x + 1) = 6x + 1

• 2x + 1 = 6x + 1

• 3(2x + 1) = 5x - 3

Solve the equation: 3(x - 1) = 2x + 9

• x = 5

• x = 8

• x = 12

• x = 15

What does it mean to isolate a variable?

• To manipulate the equation so that the variable is alone on one side, making it easy to determine its value.

• To combine all variables into one term regardless of their coefficients.

• To eliminate all constants from the equation to simplify it.

• To rearrange the equation so that all variables are on one side and constants on the other.

Solve the equation: 3x - x + 2 = 4(2x - 1)

• x = 0

• x = 1

• x = 2

• x = -1

What is the distributive property?

• The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

• The distributive property states that a + (b + c) = (a + b) + c, allowing you to add numbers in any order.

• The distributive property states that a(b - c) = ab - ac, allowing you to multiply a single term by the difference of two terms.

• The distributive property states that a(b * c) = ab * ac, allowing you to multiply a single term by the product of two terms.