Multistep Equations and INequalities

Front

What is a multistep equation?

Back

A multistep equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

Front

How do you determine if an equation has one solution, no solutions, or infinitely many solutions?

Back

To determine the number of solutions, simplify the equation. If you end up with a true statement (e.g., 0=0), there are infinitely many solutions. If you get a false statement (e.g., 0=5), there are no solutions. If you find a specific value for the variable, there is one solution.

Front

Solve the equation: 5x + 4 = 2x + 4

Back

x = 0 (One solution)

Front

Solve the inequality: 77 ≤ 5 + 8n

Back

n ≥ 9 (Graph the solution on a number line starting from 9 to the right)

Front

What does it mean if an equation has no solutions?

Back

An equation has no solutions when the simplified form leads to a contradiction, such as 0 = 5.

Front

Solve the equation: 4 - 3x = -3(x - 5) - 7

Back

No solution (the equation simplifies to a contradiction).

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

Solve the equation: 3y + 6 + 4y - 7 = -8

Back

y = -1 (One solution)

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when the simplified form results in a true statement for all values of the variable, such as 0 = 0.

Front

Solve the equation: 2x + 4 = 2x + 4

Back

Infinitely many solutions (the equation is always true).