Problem 30 Solve each equation. Check your ... [FREE SOLUTION]

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Chapter 3: Problem 30

Solve each equation. Check your solution. $$-4 x=-16$$

Short Answer

Expert verified

The solution is $x=4$.

Step by step solution

Write Down the Equation

We start with the equation given in the problem, which is \[-4x = -16\].

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Key Concepts

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

Solving Linear Equations

Solving linear equations is a fundamental skill in prealgebra, required to find the value of unknowns in mathematical statements. A linear equation is any equation that forms a straight line when graphed, and it typically includes one or more variables without exponents. To solve a linear equation like $-4x = -16$, the goal is to isolate the variable $x$ on one side of the equation.

Here's how to achieve that:

Identify the variable you need to solve for. In this case, it is $x$.
Use inverse operations to simplify the equation. This might involve adding, subtracting, multiplying, or dividing both sides by the same number.
In this example, divide both sides by $-4$ to solve for $x$:

\[x = \frac{-16}{-4} = 4\]
This means that $x = 4$ is the solution to the original equation. The key here is to perform the same operation on both sides to maintain the balance of the equation.

Negative Coefficients

In prealgebra, a coefficient is a number that multiplies a variable in an equation. A negative coefficient, such as the $-4$ in our example $-4x = -16$, often indicates that the variable is multiplied by a negative number.

When solving equations with negative coefficients, it is important to remember:

Dividing or multiplying both sides of the equation by the negative number essentially changes the sign of the elements involved.
Maintaining the balance of the equation is crucial, so whatever operation you apply to one side, you must apply to the other side too.
In our example, by dividing both sides by $-4$, we effectively transformed the negative coefficient into a positive one, making it easier to solve for $x$.

Through this process, we change the equation from a negative multiplication to a simpler form for further analysis.

Checking Solutions

Once you've found a solution to a linear equation, checking your work is a crucial step to ensure it's correct. This step involves substituting the solution back into the original equation to verify that both sides of the equation remain equal.

Let's check our solution for $x = 4$ to the equation $-4x = -16$:

Substitute $x = 4$ back into the original equation: $-4(4) = -16$.
Solve the left-hand side: $-16$.
Since $-16 = -16$, the solution holds true.

This verification process ensures precision in mathematics and demonstrates how each step logically flows in solving and confirming linear equations. It provides confidence that the solution is correct and reinforces understanding.

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91影视

Solve each equation. Check your solution. $$-4 x=-16$$

Short Answer

Step by step solution

Write Down the Equation

Key Concepts

Solving Linear Equations

Negative Coefficients

Checking Solutions

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