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Chapter 1: Problem 55

Simplify each expression. $$ 6 t+8-6 t+3 $$

Short Answer

Expert verified
The simplified expression is 11.

Step by step solution

01

Identify like terms.

Look at the given expression: 6t + 8 - 6t + 3. Identify the terms that are alike. In this case, 6t and -6t are like terms because they both have the variable 't'.
02

Combine like terms.

Combine the like terms identified in the previous step: 6t - 6t. Combine these to get 0.
03

Combine constants.

Now, add the constant terms together: 8 + 3. This simplifies to 11.
04

Write the simplified expression.

Combine the results from the previous steps: 0 + 11 = 11.So, the simplified expression is simply 11.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

like terms
In algebraic expressions, **like terms** are terms that have the same variable raised to the same power. For example, in the expression 6t + 8 - 6t + 3, the terms 6t and -6t are like terms because they both contain the variable 't' with the power of one. Unlike terms, on the other hand, do not share the same variable or the same power. Identifying like terms is essential because it allows you to simplify the expression more efficiently. Once identified, these terms can be combined by adding or subtracting their coefficients.
combining like terms
The process of **combining like terms** involves adding or subtracting the coefficients of the like terms. For example, in the expression 6t + 8 - 6t + 3, the like terms are 6t and -6t. When we combine these, we get: 6t - 6t = 0. This simplification helps to reduce the complexity of the expression. The method is straightforward:
  • Group all the like terms together.
  • Add or subtract their coefficients.
  • Simplify the resulting expression.
This process makes it easier to handle and understand the equation better.
constants in algebra
The term **constants in algebra** refers to numbers that stand alone without any variables attached to them. In our example, the constants are 8 and 3. Constants are important because they can be easily combined through addition or subtraction. For instance, in the given expression 6t + 8 - 6t + 3, after combining the like terms (6t - 6t = 0), we are left with only the constants: 8 + 3. This results in 11. Working with constants is usually very simple, as it only involves basic arithmetic.
When you combine constants in an expression, you simplify it further, making it more manageable and easier to understand.

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Most popular questions from this chapter

A manufacturer has fixed costs of \(\$ 1000\) to produce gizmos. Each gizmo costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the total cost to make \(x\) gizmos and \(y\) gadgets.

Use the distributive property to rewrite each expression. $$ -3(2 x-5) $$

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Write a numerical expression for each phrase, and simplify the expression. The product of 12 and the difference of 9 and -8
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