Solving Equations with Distributive Property

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

How do you apply the distributive property to the expression 6(b - 4)?

Back

You apply the distributive property by multiplying 6 by both b and -4, resulting in 6b - 24.

Front

What is the first step to solve the equation 2(a + 4) = 12?

Back

The first step is to apply the distributive property: 2a + 8 = 12.

Front

How do you isolate the variable in the equation 4(c + 7) = 20 after applying the distributive property?

Back

After applying the distributive property, you subtract 28 from both sides to isolate the variable.

Front

What is the solution to the equation 2(6k - 1) = -38?

Back

The solution is k = -3.

Front

What is the next step after simplifying 3(2x + 5) = 39?

Back

After simplifying, you would isolate x by first subtracting 15 from both sides.

Front

What does it mean to isolate a variable in an equation?

Back

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

Front

What is the result of applying the distributive property to the expression 5(3 + 2x)?

Back

The result is 15 + 10x.

Front

How can you check your solution for the equation 3(2x + 5) = 39?

Back

You can check your solution by substituting the value of x back into the original equation to see if both sides are equal.

Front

What is the importance of the distributive property in solving equations?

Back

The distributive property is important because it allows you to simplify expressions and solve equations more easily.