Solving Equations and Inequalities

What is the error in the following steps: 19 - 2k = 3k - 1; +3k; 19 + 1k = -1; -19; k = -20?

• The error is that instead of adding 3k, they should have subtracted 3k.

• The error is in the calculation of 19 + 1k.

• The error is that they should have added 2k instead of subtracting it.

• The error is that they forgot to simplify the equation.

What is a variable in mathematics?

• A symbol used to represent a known value in an equation or expression.

• A constant that does not change in an equation.

• A symbol used to represent an unknown value in an equation or expression.

• A type of mathematical operation.

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

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

• Multiply both sides of the equation by the same number.

• Add the same value to both sides of the equation.

• Graph the equation and see if the solution lies on the line.

What is an equation?

• An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

• An equation is a type of inequality that shows the relationship between two numbers.

• An equation is a graphical representation of a mathematical function.

• An equation is a numerical value that represents a constant.

What is an inequality?

• A mathematical statement that shows two expressions are equal.

• A mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

• A type of equation that has no solution.

• A graphical representation of a function.

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

• y = 2

• y = 3

• y = 4

• y = 5

What is the first step in solving the equation 5x + 15 = 10x - 40?

• Move all terms involving x to one side and constant terms to the other side.

• Add 40 to both sides of the equation.

• Subtract 5x from both sides of the equation.

• Divide both sides by 5.

What is the process of solving inequalities?

• It involves finding the roots of the equation only.

• Similar to equations, but when multiplying or dividing by a negative number, the inequality sign must be flipped.

• Inequalities can only be solved graphically.

• The process is the same as solving linear equations without any exceptions.

What is the solution to the equation 4k + 24 = 6k - 10?

• k = 12

• k = 15

• k = 17

• k = 20

How do you isolate a variable in an equation?

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

• By performing inverse operations on both sides of the equation to get the variable alone on one side.

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

• By dividing both sides of the equation by the coefficient of the variable.