Problem 66 Solve the equations. $$-16=\fr... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 4: Problem 66

Solve the equations. $$-16=\frac{t}{4}-14$$

Short Answer

Expert verified

The solution is $ t = -8 $.

Step by step solution

- Add 14 to both sides

To isolate the term with the variable, add 14 to both sides of the equation: \[ -16 + 14 = \frac{t}{4} - 14 + 14 \] which simplifies to \[ -2 = \frac{t}{4} \]

- Multiply both sides by 4

To solve for the variable, multiply both sides by 4 to cancel out the fraction: \[ -2 \times 4 = \frac{t}{4} \times 4 \] which simplifies to \[ t = -8 \]

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Key Concepts

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

Isolating Variable

One of the key skills in solving linear equations is isolating the variable. This means rearranging the equation so the variable stands alone on one side of the equation.

In our example, \[ -16 = \frac{t}{4} - 14 \], you first need to get $\frac{t}{4}$ by itself. To do this, we add 14 to both sides. Doing so eliminates the -14 on the right side of the equation:

\[ -16 + 14 = \frac{t}{4} - 14 + 14 \] which simplifies to: \[ -2 = \frac{t}{4} \]

By isolating the variable term, we make it easier to solve for the unknown variable.

Equation Simplification

Equation simplification involves making the equation easier to manage by reducing complexity.

For the equation \[ -2 = \frac{t}{4} \], the next step is to eliminate the fraction. We do this by multiplying both sides by 4, the denominator of the fraction:

\[ -2 \times 4 = \frac{t}{4} \times 4 \] which simplifies to \[ t = -8 \]

Multiplying by 4 cancels out the fraction, leaving us with the simplified equation $ t = -8 $. Now, the variable is isolated and simplified to its basic form.

Basic Algebra Steps

Understanding the basic algebra steps is crucial for solving linear equations successfully. Here are the fundamental steps involved:

Identify the variable and terms involving the variable.
Use addition or subtraction to move all constant terms to the opposite side of the equation.
Isolate the variable term by removing coefficients using multiplication or division.

Applying these steps to our example:

We identify the variable $\frac{t}{4}$ and constants -16 and -14.
We add 14 to both sides to move the constant term: \[ -16 + 14 = \frac{t}{4} - 14 + 14 \] which simplifies to: \[ -2 = \frac{t}{4} \]
We then isolate the variable $t$ by multiplying both sides by 4: \[ -2 \times 4 = \frac{t}{4} \times 4 \]
Resulting in the solution $ t = -8 $

By following these basic steps, solving linear equations becomes a straightforward process.

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91影视

Solve the equations. $$-16=\frac{t}{4}-14$$

Short Answer

Step by step solution

- Add 14 to both sides

- Multiply both sides by 4

Key Concepts

Isolating Variable

Equation Simplification

Basic Algebra Steps

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