Solving Linear Equations

What does it mean to distribute in an equation?

• To add a term inside the parentheses to the term outside.

• To multiply a term outside the parentheses by each term inside the parentheses.

• To divide a term inside the parentheses by the term outside.

• To subtract a term inside the parentheses from the term outside.

Solve for x: 5 + 3x = 8x - 15

• x = 2

• x = 3

• x = 4

• x = 5

What is a linear equation?

• A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

• A linear equation is an equation that represents a straight line on a graph, typically in the form y = mx + b.

• A linear equation is an equation that can have exponents greater than one, such as x^2 + y^2 = 1.

• A linear equation is a polynomial equation of degree two or higher.

Solve for x: 7x - 3x - 8 = 24

• x = 6

• x = 7

• x = 8

• x = 9

How can you check if x = 4 is a solution for the equation 5 + 3x = 8x - 15?

• Substitute x = 4 into the original equation: 5 + 3(4) should equal 8(4) - 15. If both sides are equal, x = 4 is a solution.

• Calculate the value of x by rearranging the equation to isolate x on one side.

• Check if 5 + 3(4) equals 8(4) + 15 instead of subtracting 15.

• Use a graphing calculator to find the intersection of the two sides of the equation.

What does it mean to solve a linear equation?

• To find the value of the variable that makes the equation true.

• To graph the equation on a coordinate plane.

• To determine the slope of the equation.

• To rewrite the equation in standard form.

What is the next step after combining like terms in the equation 8x + 2 + 3x + 5 = x + 12?

• Isolate the variable x by moving all x terms to one side and constant terms to the other.

• Add 5 to both sides of the equation.

• Multiply both sides of the equation by 2.

• Subtract 2 from both sides of the equation.

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

• Combine like terms on the left side to simplify the equation, then isolate x.

• Multiply both sides by 7 and then add 8.

• Subtract 24 from both sides and then divide by 4.

• Add 3x to both sides and then simplify.

What is the general form of a linear equation?

• Ax + By = C, where A, B, and C are constants.

• y = mx + b, where m is the slope and b is the y-intercept.

• y = ax^2 + bx + c, where a, b, and c are constants.

• Ax^2 + By^2 = C, where A, B, and C are constants.

Solve for x: 7x + 19 = -2x + 55

• x = 2

• x = 3

• x = 4

• x = 5