24-25 Algebra 1 Solving Linear Equations

Front

What is a coefficient in an equation?

Back

A coefficient is a numerical factor that multiplies a variable in an algebraic expression. For example, in the equation 4x + 6 = 180, the coefficient of x is 4.

Front

How do you solve the equation 3(x-4) = -3?

Back

To solve, first distribute: 3x - 12 = -3. Then add 12 to both sides: 3x = 9. Finally, divide by 3: x = 3.

Front

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

Back

To solve, first rearrange: 5x - 8x = 4 + 14. This simplifies to -3x = 18. Dividing by -3 gives x = -6.

Front

How do you solve for k in the equation 2k + 4 = 180?

Back

Subtract 4 from both sides: 2k = 176. Then divide by 2: k = 88.

Front

What is the solution to the equation 6(n - 2) = 3n + 12?

Back

Distribute: 6n - 12 = 3n + 12. Rearranging gives 6n - 3n = 12 + 12, so 3n = 24. Dividing by 3 gives n = 8.

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 other side.

Front

What is the first step in solving linear equations?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms and eliminating parentheses.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It has the form ax + b = c, where a, b, and c are constants.

Front

How do you check your solution to a linear equation?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

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

Back

The distributive property allows you to multiply a single term by each term inside a set of parentheses, helping to simplify equations.