Solving multi-step problems using linear equations in one variable

Front

What is a linear equation in one variable?

Back

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step to solve the equation y = mx + b for x?

Back

Subtract b from both sides to isolate the term mx.

Front

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

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

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

Back

In the equation y = mx + b, 'b' represents the y-intercept of the line.

Front

How do you solve for y in the equation ax + by = c?

Back

Rearrange the equation to isolate y: y = (c - ax)/b.

Front

What is the solution to the equation 3y = -5x + 10?

Back

To solve for y, divide all terms by 3: y = (-5/3)x + (10/3).

Front

What is the next step to solve for d in the equation 2d - 1 = s?

Back

Add 1 to both sides to isolate the term 2d.

Front

What is the solution for x in the equation m - x = n - p?

Back

Rearranging gives x = m - n + p.

Front

What is the purpose of dividing both sides of an equation by a number?

Back

Dividing both sides by a number helps to isolate the variable and maintain the equality of the equation.