Solving Simple Linear Equations

Hi there. In this math guide, I cover solving simple linear equations. Algebra for younger students from grades 5 to 8 sounds scary but if it presented and taught in a simple way the material is not as scary.

Topics

• The Letter x As Unknown Or Blank
• Addition & Subtraction Examples
• Multiplication Examples
• Division Examples

The Letter x As Unknown Or Blank

Before getting into the letter x representing an unknown or missing number, I want to show a few simple examples.

For 3 + __ = 5 the answer to the blank is 2 as three plus two does give five. Instead of blank that can be replaced by the letter or variable x. The question would be 3 + x = 5 with the answer as x = 2.

With 2 x ___ = 10 the answer to the blank is 5. Instead of using a blank replace it with x. You would have 2x = 10 with the answer of x = 5.

Addition & Subtraction Examples

Here are some examples that deal with addition and subtraction.

Example One

Solve for x from x + 5 = 10.

Think of it as something plus 5 gives 10. In this example the answer is 5 so x = 5.

Example Two

From 2 + x = -5, what is the value of x?

For this question think of it as two plus something equals negative five. This example is a little bit more difficult as you have negative numbers. If your number sense is good you know that the answer is negative 7 or x = -7.

To solve this in a more algebraically you would subtract both sides by 2. This would give x = -5 -2 which is `x = -7. Picture screenshot below.

Example Three

Solve for x in x - 8 = 10.

This subtraction example is simple. Think of it as something minus 8 equals 10. The answer here is 18.

Example Four

What is x from the equation 10 - x = 5.

This is ten minus what number is equal to five. The number sense approach would give an answer of 5.

The algebraic approach would be isolate for positive x. This would be done by moving subtracting both sides by five. You would get 10 - 5 - x on the left side and the right side would be 5 - 5 which is zero.

The negative x on the left needs to be dealt with. Add x on both sides. This would result in 10 - 5 = 5 on the left side with the right side being just x. The answer is x = 5.

Multiplication Examples

Example One

What is the value of x from the equation 5x = 50?

Five times something equals fifty is the thinking here. The answer here is x = 10.

The algebra approach would be to divide both sides by 5 to obtain the same answer of x = 10.

Example Two

From the equation 3x = 17, what is the value of x?

The number sense approach of three times something is equal to seventeen is not recommended here. It is easier to do the algebraic approach and divide both sides by 3.

Division Examples

Example One

Given the equation of x ÷ 2 = 5, what is the value of x?

Something divided by 2 is equal to 5. This something is ten.

Example Two

In this example the variable is in the denominator (bottom of fraction). With the equation of 28 ÷ x = 4, what is the value of x?

You could do the number sense approach and ask yourself 28 divided by something gives 4. The answer here is 7. With the algebra approach multiply both sides by x as the x is in the denominator. The equation is now 28 = 4x. Divide both sides by 4 to obtain x = 7.

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