Solving Equations

Front

What is an equation?

Back

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

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 3(x - 2) = 18?

Back

Distribute the 3 to both terms inside the parentheses: 3x - 6 = 18.

Front

How do you isolate the variable in the equation 4x + 3 = -5?

Back

Subtract 3 from both sides to get 4x = -8, then divide by 4 to find x = -2.

Front

Back

First, simplify to get 14x - 28 = 42. Then, add 28 to both sides to get 14x = 70, and divide by 14 to find x = 5.

Front

What is the formula for the total cost of hiring a mechanic who charges a flat fee and an hourly rate?

Back

The formula is y = 65x + 15, where y is the total cost, x is the number of hours, and 15 is the flat fee.

Front

Back

Multiply both sides by 5 to isolate x, resulting in x = 10.

Front

What is the purpose of using variables in equations?

Back

Variables represent unknown values that can change, allowing us to express general relationships and solve for specific values.

Front

What does it mean to check your solution after solving an equation?

Back

Checking your solution means substituting the found value back into the original equation to verify that both sides are equal.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one and graphs as a straight line.