An **algebraic sentence** as soon as written in equation type involves algebraic expression (which contain variables such as letter in the alphabet), constants, and also an equal symbol. Each algebraic sentence might contain a combination of algebraic expressions and constants, or with simply two or much more algebraic expressions. Practically always, words “is” in one algebraic sentence denotes the price of equality.

In our instance above, the algebraic sentence, “**Five an ext than double a number is forty-three**“, is translated and also written right into its equation form: 2x + 5 = 43.

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But prior to we delve right into solving word troubles that indicate algebraic sentences, it’s critical that we come to be familiar with just how to translate and write algebraic expressions.

## Algebraic Expressions

Learning exactly how to write and translate algebraic expressions is the structure in composing algebraic sentences. Eventually, us will use this expertise to create algebraic equations wherein we deal with for the worth of the unknown variable.

**What is one algebraic expression?**

Think of an algebraic expression as the equivalent of a expression in the English language. It does no convey a complete thought yet is an important building block in constructing a sentence. Algebraic expression consist the numbers, variables, and arithmetic operations.

Let’s take a fast look at part math phrases the were translated and also written into algebraic expressions.

the sum of a number and 8 \\large\\,\\,\\, \\to \\,\\,\\,\\, \\colorredc + 8 3 less than a number \\large\\,\\,\\, \\to \\,\\,\\,\\, \\colorredy - 3 the product of 45 and also m \\large\\,\\,\\, \\to \\,\\,\\,\\,\\colorred45m a number divided by 2 \\large\\,\\,\\, \\to \\,\\,\\,\\,\\Large \\colorredx \\over 2### Translating and also Writing Algebraic Sentences

Once girlfriend know exactly how to interpret math phrases into algebraic expressions, it’ll be basic for you come translate and write algebraic sentences in one equation type as well.

For instance, how do you create “**the difference of 16 and k is seven**” into an algebraic equation?

Let’s deconstruct this algebraic sentence.

You may notification that we interpreted “the difference of 16 and k” right into an algebraic expression, 16-k, then supplied the equal symbol (=) in ar of the word “is”.

As I stated at the beginning of this lesson, the word “is” in one algebraic sentence, many of the time, signifies the equality symbol which is the instance in this example.

Therefore, we deserve to write this algebraic sentence in equation kind as 16 - k = 7.

Now that we are confident in translating algebraic sentences and writing them in one equation format, it’s time for us to take one step further. We will not only translate and write algebraic sentences into algebraic equations but also proceed to resolve them.

### Examples that Algebraic sentence Word Problems

The main crucial when fixing word problems with algebraic sentence is to accurately translate the algebraic expression then collection up and also write each algebraic equation correctly. In act so, we have the right to ensure that us are fixing the best equation and as a result, will get the exactly answer because that each word problem.

**Example 1:** Six much more than seven times a number is thirty-four. Uncover the number.

First, let’s decoding the algebraic sentence. It’s crucial that us identify and separate the algebraic expressions from the constants as well as determine if the problem says equality between the terms.

For the unknown value, we’ll usage \\largex as our variable.

**Note:** Since addition is commutative, transforming the bespeak of the addends on the left next of the equation go not change the sum. Therefore, we may additionally write the algebraic expression together 7x+6 or the algebraic equation together 7x + 6 = 34 instead.

However, because that our discussion, us will usage 6 + 7x = 34 together our equation.

The original trouble asks united state to discover the number i beg your pardon in this case is \\largex. Therefore our next step is to resolve for \\largex in ours equation, 6 + 7x = 34.

Solution:

Now, we’ll evaluate the value of \\largex = 4 to verify if the number we discovered satisfies the initial algebraic sentence.

Remember the we space asked to uncover the identity of “the number” in our algebraic sentence and also NOT the value of the change \\largex. Therefore, it will be incorrect come say the \\largex=4 is the answer. This is a typical mistake the we always need to pay fist to.

We’ll change the variable \\largex v the number 4 to check out if the algebraic expression ~ above the left next of the equation likewise results to 34.

Yes, it does! This method that **number 4 is the answer**.

**Example 2: **The difference between three time a number and also five is sixteen. Discover the number.

Right away, the word “difference” in ours algebraic sentence provides us a clue that we will be using the individually operation. But, unlike, in addition, the bespeak of the terms within one expression matters in subtraction. So we have to make sure that the state in ours algebraic expression are collection up in the exactly order.

Another keyword is “times”, which suggests that 3 is being multiplied come a number whose worth is currently unknown.

This time, let’s use \\largeg together our variable. Begin by translating the algebraic expression appropriately then continue to compose the equation.

Now that we have our equation, let’s discover out what the unknown value is by fixing for the variable, \\largeg.

Solution:

As disputed in our an initial example, it is vital that we verify if the an outcome of our solution provides the algebraic equation true. For this one, I will certainly leave it up to you to advice the value of \\largeg = 7. Remember to change the unknown value of the variable \\largeg with the number 7 to view if the left side of the equation is likewise equal to 16.

Since the initial algebraic sentence needs us to uncover the number, climate **the prize is number 7**.

**Example 3:** A number decreased by half of the number is four. Find the number.

This algebraic sentence is fairly interesting since we don’t just have one unknown value, however two! First, we have actually the “number” (the unknown) climate the “half that the number”, which way one-half that the unknown.

The keyword “half of” also indicates multiply something by one-half when the “decreased by” tells united state that we will be subtracting one term native the other.

To organize our thoughts, let’s deconstruct this algebraic sentence into its meat and potatoes.

Being maybe to rest apart our algebraic sentence right into its an easy parts allows us to check out the sentence thoroughly and also understand the relationship between its quantities.

After setup up ours algebraic equation, our next step is to fix it for \\largem.

Solution:

We should evaluate the worth of \\largem = 8 to check if the number we obtained makes ours algebraic equation true.

Great! The worths on both sides of the equation room equal to each other. Therefore, the **number 8 is the exactly answer** to our initial algebraic sentence.

**Example 4:** 4 times the amount of double a number and also six is thirty-two. Find the number.

Looking closely, we view a couple of keywords the would assist us in translating this algebraic sentence into an equation.

**times**– method that we’ll be multiply 4 by the quantity, “sum of double a number and six”

**sum**– method that we need to include the terms, “twice a number” and also six

**twice**– method that a number (the unknown value) is multiplied by 2

With this in mind, let’s create our algebraic equation.

Notice the we used the change \\larged in our equation to stand for ours unknown value. Let’s currently proceed and solve for \\larged and afterward, check if the value we acquire indeed provides the equation true.

Solution:

Evaluate the value of \\larged = 1:

Looks like every little thing checks out, for this reason **the price **to ours algebraic sentence is the **number 1**.

**Example 5:** Two-thirds that the amount of three times a number and also six is ten. What is the number?

This problem involves a portion and an algebraic expression together you deserve to tell. The keyword “of” indicates multiplication, so that tells us that we have to multiply the fraction \\large2 \\over 3 through the sum of the two provided quantities (“three time a number” and also six).

Let’s relocate on and write ours algebraic equation. We’ll use the variable \\largey as the placeholder because that our “number” whose value is right now unknown.

Awesome! We room able to interpret our algebraic sentence right into an equation. It’s time for united state to fix for \\largey climate I’ll leave it up to you to carry out a inspect if the number we uncover as the worth of \\largey makes the algebraic equation true.

Solution:

Once you evaluate \\largey = 3, you’ll check out that **the answer** to our word problem is indeed the **number 3**.

**Example 6:** twice the difference of a number and three is four more than the number. Find the number.

We have an example here that is a small different from the word troubles we’ve covered so far. In this algebraic sentence, both sides of the equation save on computer an algebraic expression. However, the keywords existing will help us analyze it correctly right into an equation so there’s naught to concern about.

Keywords:

**twice**– method that we will multiply the quantity (difference that a number and also three) by 2

**difference**– tells us to use the subtraction operation in between our unknown worth (“number”) and also three

**more than**– way that we require to add four to our unknown value

Let’s settle for our unknown value, \\largea, climate verify that our result makes the algebraic equation true.

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Solution:

Evaluate the value of \\largea = 10:

Perfect! The worth we acquired for \\largea which is 10, made our equation equal on both sides. Thus, **the prize is the number 10**.