solve linear equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side. This often involves adding, subtracting, multiplying, or dividing.

Front

What is the solution to the equation 3x + 6 = 21?

Back

x = 5.

Front

What steps would you take to solve the equation 5 + 3x = 8x - 15?

Back

1. Subtract 3x from both sides: 5 = 5x - 15. 2. Add 15 to both sides: 20 = 5x. 3. Divide by 5: x = 4.

Front

What is the solution to the equation x - 23 = 17?

Back

x = 40.

Front

How do you solve the equation 2(3x + 4) + 2 = 4 + 3x?

Back

1. Distribute: 6x + 8 + 2 = 4 + 3x. 2. Combine like terms: 6x + 10 = 4 + 3x. 3. Subtract 3x from both sides: 3x + 10 = 4. 4. Subtract 10: 3x = -6. 5. Divide by 3: x = -2.

Front

What is the solution to the equation 4x + 1 = 7x - 5?

Back

x = 2.

Front

What is the importance of checking your solution in a linear equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming that it is correct.

Front

What does it mean for two linear equations to be equivalent?

Back

Two linear equations are equivalent if they have the same solution set, meaning they represent the same line on a graph.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.