Solving Linear Equations

Front

What is a linear equation?

Back

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

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable (usually x) that makes the equation true.

Front

What is the first step in solving the equation 2 - 4x = 3x - 12?

Back

The first step is to combine like terms and isolate the variable on one side of the equation.

Front

Solve for x: 2 - 4x = 3x - 12

Back

x = 2

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you apply the distributive property to the equation 2(3x + 4) + 2 = 4 + 3x?

Back

You distribute 2 to both 3x and 4, resulting in 6x + 8 + 2 = 4 + 3x.

Front

Solve for x: 2(3x + 4) + 2 = 4 + 3x

Back

x = -2

Front

What does 'eight less than three times a number' mean mathematically?

Back

It means 3x - 8, where x is the number.

Front

Translate the phrase 'ten more than one and half times the same number' into an equation.

Back

1.5x + 10.

Front

What is the equation formed by 'eight less than three times a number is equivalent to ten more than one and half times the same number'?

Back

3x - 8 = 1.5x + 10.