Solving Equations and Inequalities

Front

What is an equation?

Back

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

Front

What is an inequality?

Back

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

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving the equation 5x + 9 = 2x - 3?

Back

The first step is to isolate the variable by moving all terms involving x to one side and constant terms to the other.

Front

How do you combine like terms in an equation?

Back

You combine like terms by adding or subtracting the coefficients of terms that have the same variable raised to the same power.

Front

What is the purpose of adding or subtracting the same number from both sides of an equation?

Back

Adding or subtracting the same number from both sides maintains the equality of the equation.

Front

What is the solution to the equation 5x + 15 = 10x - 40?

Back

x = 11.

Front

What operation is performed to isolate x in the equation 3x + 9 = -3?

Back

Subtract 9 from both sides.

Front

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

Back

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

Front

What does it mean to check your solution in an equation?

Back

To check your solution means to substitute the value back into the original equation to verify that both sides are equal.