Solve Equations Mixed Review

Front

What is the first step to solve 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 combine like terms in the equation 5x - 4 + 2x = 3?

Back

Combine the x terms: (5x + 2x) - 4 = 3, which simplifies to 7x - 4 = 3.

Front

What is the process to isolate n in the equation 50 = -5(6n + 8)?

Back

First, divide both sides by -5 to get -10 = 6n + 8, then subtract 8 from both sides to isolate the term with n.

Front

What is the solution to the equation 5x - 14 = 8x + 4?

Back

Rearranging gives -14 - 4 = 8x - 5x, which simplifies to -18 = 3x, leading to x = -6.

Front

What does it mean to solve for a variable in an equation?

Back

To solve for a variable means to isolate that variable on one side of the equation to find its value.

Front

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

Back

Checking your solution ensures that the value satisfies the original equation, confirming its correctness.

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form ax + b = c.

Front

How do you handle equations with parentheses?

Back

Use the distributive property to eliminate parentheses by multiplying the term outside the parentheses by each term inside.

Front

What is the significance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides of the equation have the same value.

Front

What is the method to solve for x in the equation 5x - 14 = 8x + 4?

Back

Rearrange the equation to isolate x by moving all x terms to one side and constant terms to the other.