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Chapter 6: Problem 45

Solve. $$ 0.64 \cdot x=170 $$

Short Answer

Expert verified
x = 265.625

Step by step solution

01

Understand the Equation

The given equation is a linear equation involving a single variable, x. It looks like this: \[0.64 \times x = 170\] The goal is to solve for x.
02

Isolate the Variable

To isolate x, divide both sides of the equation by 0.64: \[\frac{0.64 \times x}{0.64} = \frac{170}{0.64}\] Simplifying, we get: \[x = \frac{170}{0.64}\]
03

Perform the Division

Perform the division to find the value of x: \[x = 265.625\]

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Key Concepts

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

linear equations
Linear equations are mathematical statements that show the equality between two expressions with a linear relationship. This means the variable (usually denoted as x) does not have an exponent other than 1. In the example given, the linear equation is \(0.64 \times x = 170\).
Such equations can be visualised as straight lines if plotted on a graph. The equation tells you that 0.64 times some number (x) equals 170 and your task is to figure out what that number is.
variable isolation
To solve a linear equation like \(0.64 \times x = 170\), you need to isolate the variable x. This makes it the subject of the equation, leaving you with x equals some number on the other side. Isolating the variable involves reversing operations being performed on x.
In this case, x is being multiplied by 0.64. To undo this multiplication, you need to divide both sides of the equation by 0.64, which leaves you with:
\[x = \frac{170}{0.64}\]
division
Division is the mathematical operation used to find out how many times one number is contained within another. In this exercise, we divide 170 by 0.64 to isolate x and solve the equation.
You perform the division like this:
\[x = \frac{170}{0.64} = 265.625\].
This tells you that if you multiply 265.625 by 0.64, you get 170, thus confirming that \(x = 265.625\) is the correct solution.

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