Solving Equations with Distributive Property

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.

Front

How do you apply the Distributive Property to -7(8 + x)?

Back

You multiply -7 by both 8 and x: -7 * 8 + (-7) * x = -56 - 7x.

Front

What is the first step in solving the equation -7(8 + x) = -98?

Back

Apply the Distributive Property: -56 - 7x = -98.

Front

How do you isolate the variable x in the equation -56 - 7x = -98?

Back

Add 56 to both sides: -7x = -98 + 56, which simplifies to -7x = -42.

Front

What do you do next after -7x = -42?

Back

Divide both sides by -7: x = -42 / -7, which simplifies to x = 6.

Front

What is the solution to the equation -3(3 + 5x) = -24?

Back

First, apply the Distributive Property: -9 - 15x = -24. Then isolate x to find x = 1.

Front

How do you solve the equation 5(-7 - 7x) = 315?

Back

Apply the Distributive Property: -35 - 35x = 315. Then isolate x to find x = -10.

Front

What is the solution to the equation -3(1 + 3x) = -57?

Back

First, apply the Distributive Property: -3 - 9x = -57. Then isolate x to find x = 6.

Front

How do you solve the equation 4(7 + 6x) = 268?

Back

Apply the Distributive Property: 28 + 24x = 268. Then isolate x to find x = 10.

Front

What is the importance of checking your solution after solving an equation?

Back

Checking your solution ensures that the value of x satisfies the original equation, confirming that your solution is correct.