Solving Linear Equations

What does it mean to solve an equation?

• To find the value(s) of the variable(s) that make the equation true.

• To rewrite the equation in a different form.

• To graph the equation on a coordinate plane.

• To determine the number of solutions an equation can have.

What does it mean to have a variable on both sides of an equation?

• It means the equation is unsolvable.

• It means you need to rearrange the equation to isolate the variable, often by adding or subtracting the variable from both sides.

• It indicates that the equation is balanced and does not require any changes.

• It suggests that the variable can be ignored in the equation.

What is a constant in a linear equation?

• A variable that can change value

• A fixed value that does not change

• A term that represents the slope

• An equation that has no solution

What is the purpose of combining like terms in an equation?

• To make the equation more complex

• To simplify the equation, making it easier to solve for the variable.

• To eliminate the variable from the equation

• To change the equation into a different form

What is the solution to the equation 7x - 3x - 8 = 24?

• x = 5

• x = 6

• x = 7

• x = 8

How do you check if your solution to a linear equation is correct?

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

• By graphing the equation and checking the intersection point.

• By calculating the slope of the equation.

• By finding the roots of the equation using the quadratic formula.

What is the first step in solving the equation 3w + 5 = 14?

• Subtract 5 from both sides of the equation.

• Add 5 to both sides of the equation.

• Multiply both sides by 3.

• Divide both sides by 3.

What are inverse operations?

• Operations that have no effect on each other.

• Pairs of operations that undo each other, such as addition and subtraction or multiplication and division.

• Operations that can be performed in any order.

• Operations that always result in a positive number.

What is the significance of the equal sign in an equation?

• It indicates that the expressions on both sides of the equation are equivalent.

• It shows the operation to be performed on the numbers.

• It separates the variables from the constants.

• It indicates the beginning of a mathematical expression.

What is the solution to the equation 4x + 1 = 7x - 5?

• x = 1

• x = 2

• x = 3

• x = 4