Multi-Step Equations & Inequalities

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

Front

What does it mean to distribute in an equation?

Back

Distributing means to multiply a term outside the parentheses by each term inside the parentheses.

Front

Solve the equation: 2a - 4(a - 5) = 10

Back

Distribute -4 to a and -5: 2a - 4a + 20 = 10, then combine like terms: -2a + 20 = 10, subtract 20 from both sides: -2a = -10, divide by -2: a = 5.

Front

What is the first step in solving the equation 3(2e + 5) + 8(1 - e) = 1?

Back

Combine like terms after distributing: 6e + 15 + 8 - 8e = 1.

Front

What is the solution to the equation -15 = 5a + 12 - 2a + 6?

Back

Combine like terms: -15 = 3a + 18, then isolate a: 3a = -33, so a = -11.

Front

What does it mean to solve an inequality?

Back

Solving an inequality means finding the values of the variable that make the inequality true.

Front

Solve the inequality: 4(b + 3) - 6 ≤ -2

Back

Distribute: 4b + 12 - 6 ≤ -2, simplify: 4b + 6 ≤ -2, subtract 6: 4b ≤ -8, divide by 4: b ≤ -2.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

What is the solution to the equation 3x + 2(4x - 4) = 3?

Back

Distribute: 3x + 8x - 8 = 3, combine like terms: 11x - 8 = 3, add 8: 11x = 11, divide by 11: x = 1.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the other side.