Unit 5 Solving Equations

Front

What is the first step in solving the equation 2x + 3(5x - 7) = 47?

Back

Distribute the 3 to both terms inside the parentheses: 2x + 15x - 21 = 47.

Front

How do you isolate the variable x in the equation 3(4r - 1) + 5 = 26?

Back

First, simplify the left side: 12r - 3 + 5 = 26, then combine like terms to get 12r + 2 = 26, and finally isolate r.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

In the equation 3x + 2(4x - 4) = 3, what is the result of distributing the 2?

Back

Distributing the 2 gives 3x + 8x - 8 = 3.

Front

What is the solution to the equation 8v - 4(v + 8) = 8?

Back

The solution is v = 10 after simplifying and isolating v.

Front

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

Back

To verify that the solution satisfies the original equation and is correct.

Front

How do you solve the equation 2(x + 3) = 8?

Back

First, distribute the 2 to get 2x + 6 = 8, then isolate x by subtracting 6 and dividing by 2.

Front

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

Back

The distributive property allows you to eliminate parentheses and simplify expressions, making it easier to isolate variables.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + B = C, where A, B, and C are constants.

Front

What does it mean for an equation to be balanced?

Back

An equation is balanced when both sides are equal, meaning any operation performed on one side must also be performed on the other.