Multi-Step Equations Error Analysis

Front

What is an identity equation?

Back

An identity equation is an equation that is true for all values of the variable. For example, the equation 2(x + 3) = 2x + 6 is an identity.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that make the equation true. For example, the equation 2x + 3 = 2x + 5 has no solution.

Front

How do you determine the number of solutions for a linear equation?

Back

To determine the number of solutions, simplify the equation. If you end up with a true statement (like 0 = 0), it has infinitely many solutions (identity). If you get a false statement (like 0 = 5), it has no solution.

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

Front

Solve the equation: 5h - 7 = 5(h - 2) + 3

Back

Identity (true for all h).

Front

Write the equation for a hang glider descending at 2 m/s from 25 m above ground after t seconds.

Back

h = -2t + 25.

Front

Solve the equation: 5 + 2(n + 1) = 2n

Back

No Solution.

Front

Solve the equation: 6.78x - 5.2 = 4.33x + 2.15

Back

x = 3.

Front

How do you solve a multi-step equation?

Back

1. Simplify both sides of the equation. 2. Use inverse operations to isolate the variable. 3. Check your solution by substituting it back into the original equation.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.