Solving Linear Equations

This set of flashcards covers solving linear equations, including those with parentheses, fractions, and application problems.

What is the first step to solving linear equations when parentheses are present?

Remove the parentheses using distribution (multiplying the value in front of the parentheses through the entire expression inside).

What is the second step in solving linear equations?

Simplify each side of the equation by combining like terms if possible.

What is the third step in solving linear equations?

Isolate the variables to one side of the equation.

What is the fourth step in solving linear equations?

Isolate the constants to the opposite side of the equation from the variables.

What is the fifth step in solving linear equations?

Solve for the variable through multiplication or division, if needed.

When combining terms, what should you do with the signs?

Use the signs that you see and combine as necessary.

When isolating variables, which side should you move your variables to?

It doesn't matter which side you move them to, but it can be easiest to move the smaller variable to the larger one.

When solving equations with fractions, what is the first step?

Find the least common multiple (LCM) of all the denominators.

After finding the LCM, what is the next step?

Multiply every term in the equation by the LCM.

When multiplying a fraction by a whole number, which part of the fraction does the whole number get multiplied to?

The top (numerator) of the fraction. The goal is to then cancel the bottom (denominator) with the multiplied number.

After clearing denominators, what should you do?

Once there are no more fractions, solve the equation as normal.

What does 'm' represent in the linear equation y = mx + b?

m represents the slope, or the rate of change.

What does 'b' represent in the linear equation y = mx + b?

b represents the y-intercept, or the starting point.

If a problem states a value is decreasing at a rate, how is that represented in an equation?

It is the slope (m) and it is given a negative value

What is the slope formula?

m = (y2 - y1) / (x2 - x1)

When calculating sales tax, what must be done with the percent?

The sales tax percent must be converted to a decimal

How do you calculate the amount of tax that will be paid?

Multiply the sales tax by the purchase amount.