/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 Solve the equations. $$7=\frac... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 22

Solve the equations. $$7=\frac{a}{-0.05}$$

Short Answer

Expert verified
a = -0.35

Step by step solution

01

Understand the Given Equation

The equation given is \( 7 = \frac{a}{-0.05} \). We need to solve for the variable \( a \).
02

Isolate the Variable

To solve for \( a \), we need to isolate it on one side of the equation. Multiply both sides by \( -0.05 \) to achieve this.
03

Perform the Multiplication

When we multiply both sides by \( -0.05 \), we get: \[ 7 \times (-0.05) = \frac{a}{-0.05} \times (-0.05) \].
04

Simplify Both Sides

Simplify the left side: \( 7 \times (-0.05) = -0.35 \). The right side simplifies to \( a \). So, we have: \( a = -0.35 \).

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Key Concepts

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

Isolating Variables
In mathematics, isolating the variable is a key step in solving equations. To isolate a variable means to get the variable by itself on one side of the equation. This often involves inverse operations. For example, if a variable is being divided by a number, you would multiply both sides of the equation by that number to move it to the other side. In our exercise, we had the equation \( 7 = \frac{a}{-0.05} \). To isolate \( a \), we multiplied both sides by \( -0.05 \). This left us with \( -0.35 = a \) after simplifying. Always remember: the goal is to get the variable alone on one side, so you can see its value clearly.
Multiplication in Equations
Multiplication in equations can be a powerful tool for solving for a variable. When faced with a variable divided by a number, multiply both sides of the equation by that number to cancel out the division. For instance, our original equation was \( 7 = \frac{a}{-0.05} \). To remove the division by \( -0.05 \), we multiplied both sides by \( -0.05 \). This operation yielded \( 7 \times (-0.05) = a \). Make sure to perform the same multiplication on both sides of the equation to maintain balance. In math, multiplying both sides by the same number ensures the equation remains true.
Simplifying Equations
Simplifying equations is the process of making the equation easier to solve. This often involves combining like terms and performing basic arithmetic operations. In our step-by-step solution, after isolating the variable and performing multiplication, we had \( 7 \times (-0.05) = a \). By simplifying the left side, we calculated \( 7 \times (-0.05) = -0.35 \). This left us with \( a = -0.35 \). Always simplify each side of the equation to its simplest form. It makes your final answer clear and easy to understand.

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