Problem 100 Solve each equation. $$ 3 t+... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 6: Problem 100

Solve each equation. $$ 3 t+2=0 $$

Short Answer

Expert verified

t = -2/3

Step by step solution

Isolate the variable term

Start by subtracting 2 from both sides of the equation to begin isolating the variable term, which is '3t'. Equation: 3t + 2 = 0 Subtract 2 from both sides: 3t = -2

Solve for the variable

Next, divide both sides of the equation by 3 to solve for 't'. Equation: 3t = -2 Divide both sides by 3: t = -2/3

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Key Concepts

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

Isolate the Variable

Isolating the variable is the first step in solving a linear equation. This means we need to get the variable by itself on one side of the equation. This helps us see clearly what the variable equals. In our exercise, the variable is 't'.

The given equation is:
\[3t + 2 = 0\]
To isolate 't', we need to get rid of the number 2 on the left side of the equation. To do this, we perform the opposite operation of addition, which is subtraction:

Subtract 2 from both sides of the equation.

Now, the equation looks like this:
\[3t + 2 - 2 = 0 - 2 \]
This simplifies to:
\[3t = -2\]
By isolating the variable, we make it easier to solve for 't'.

Linear Equations

Linear equations are equations of the first degree. This means the variable (like 't' in our example) is not raised to any power higher than 1. The general form of a linear equation is:
\[ax + b = c\]
In our specific problem, the linear equation is:

\[3t + 2 = 0\] where
\[a = 3, b = 2,\] and \[c = 0\]

Solving linear equations involves finding the value of the variable that makes the statement true. They often appear in algebra and are used in various real-life applications like calculating distances, budgeting, and more.
Understanding how to manipulate and solve these equations is an essential skill in math.

Algebraic Manipulation

Algebraic manipulation refers to the techniques used to rearrange and solve equations. It involves applying the basic arithmetic operations (addition, subtraction, multiplication, division) to both sides of an equation to solve for the unknown variable.

In our case, we started with: \[3t + 2 = 0\]
First, we subtracted 2 from both sides (algebraic manipulation) to isolate the term with 't':

\[3t = -2\]

Next, we wanted to solve for 't', so we divided both sides by 3:

\[t = \frac{-2}{3}\]

Algebraic manipulation makes it possible to transform and simplify equations, ultimately finding the value of the unknown variable.
This is a fundamental skill not only in algebra but in all higher-level math courses.

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91影视

Solve each equation. $$ 3 t+2=0 $$

Short Answer

Step by step solution

Isolate the variable term

Solve for the variable

Key Concepts

Isolate the Variable

Linear Equations

Algebraic Manipulation

One App. One Place for Learning.

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