Multi-Step Equations: One, None, or Infinite Solutions

Front

What is a multi-step equation?

Back

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

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that makes the equation true.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value for the variable that can satisfy the equation, often resulting in a contradiction.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable makes the equation true, often resulting in an identity.

Front

Solve for v: 14 + 35v = 3v + 14

Back

v = 0. The equation simplifies to 32v = 0.

Front

Solve for x: -3(x + 6) = -3(2x + 4)

Back

x = -2. The equation simplifies to -3x - 18 = -6x - 12.

Front

Solve for p: 36 - 7p = -7p + 35

Back

No solution. The equation simplifies to 36 = 35, which is a contradiction.

Front

Solve for m: 6(m+3)=2(m+5)

Back

m = 0. The equation simplifies to 6m + 18 = 2m + 10.

Front

Solve for m: 8m + 12 = 2(4m + 6)

Back

Infinite solutions. The equation simplifies to 8m + 12 = 8m + 12, which is always true.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a set of parentheses.