Solving Multi-Step Equations

In this lesson, we will look at

• Solving multi-step equations with whole numbers
• Solving multi-step equations with fractions
• Solving multi-step equations with decimals

Solving multi-step equations with whole numbers

To solve a multi-step equation, we would start by trying to simplify the equation by combining like terms and using the distributive property whenever possible.

Consider the equation 2(x + 1) – x = 5. First, we will use the distributive property to remove the parenthesis and then we can combine like terms and the isolate the variable.

Example:

Solve 2(x + 1) – x = 5

Solution:

2(x + 1) – x = 5

2x + 2 – x = 5 (use distributive property)

x + 2 = 5 (combine like terms)

x + 2 – 2 = 5 – 2

x = 3

The following video shows more examples of solving multi-step equations.

Solving Multi-Step Equations With Fractions

To solve an equation with fractions, we first try to change it into an equation without fractions. Then, we can solve it using the methods we already know.

Consider the equation . To remove the fractions, we would need to multiply each term of the equation with the LCM of the denominator. In this case, we will multiply each term with 4. The 4 will cancel and we are left with equation 2x – 12 = 3. To isolate the variable, we will add 12 to both sides and then divide by 2.

Example:

Solve

Solution:

The following video shows more examples of solving multi-step equations with fractions.

Solving Multi-Step Equations With Decimals

The steps involved in solving multi-step equations with decimals are the same as those in equations with whole numbers. The complication may lie more in the multiplication and division of decimals rather than the steps. Another method would be to multiply each term of the equation by ten (or hundred) to convert the decimals to whole numbers and then solve the equation.

The following video shows more examples of solving multi-step equations with decimals.

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