Question

If \(18+d=12\), what is the value of \(5 d\) ? A) \(-30\) B) \(-18\) C) \(-6\) D) 6

Short answer

The value of \(5d\) is \(-30\). Therefore, the answer is A) \(-30\).

Step-by-step solution

Solve the given equation for d

Subtract \(18\) from both sides of the equation \(18+d=12\). \[ d = 12 - 18 \]

Simplify the right side of the equation

Subtract 18 from 12. \[ d = -6 \]

Find the value of \(5d\) by multiplying d by 5

Now that we have the value of \(d\) as \(-6\), we can find the value of \(5d\) by multiplying \(-6\) by \(5\). \[ 5d = 5(-6) \]

Simplify the expression

Multiply \(-6\) by \(5\). \[ 5d = -30 \] The value of \(5d\) is \(-30\). Therefore, the answer is A) \(-30\).

Key concepts

Solving Equations

Solving equations is like being a detective; you're trying to find the value of an unknown that makes an equation true. An equation is a mathematical statement that shows the equality between two expressions. In the problem given, you have the equation \(18 + d = 12\).
To solve this equation, we need to isolate the variable \(d\). This means we want \(d\) by itself on one side of the equation.

• The first step in solving this equation is to remove the \(18\) from the left side. We can do this by subtracting \(18\) from both sides.
• This gives us \(d = 12 - 18\).

By solving these steps, we arrive at \(d = -6\), which is our unknown, or solution.

Linear Equations

Linear equations are equations where the highest power of the variable is one. They form a straight line when graphed. The equation we worked on, \(18 + d = 12\), is a simple linear equation.
The key property of a linear equation is that each term is either a constant or the product of a constant and a single variable.

• Linear equations can have one solution, infinitely many solutions, or no solution at all.
• In the context of the example, the equation had one solution, \(d = -6\).

Understanding linear equations is important because they form the building blocks for learning more complex types of equations.

Arithmetic Operations

Arithmetic operations are basic mathematical computations. They include addition, subtraction, multiplication, and division. In solving equations, these operations help us manipulate expressions to find the solution.
In our exercise, we applied several arithmetic operations:

• Subtraction: We subtracted \(18\) from \(12\) to find the value of \(d\). So, \(d = 12 - 18 = -6\).
• Multiplication: Once we found \(d\), we multiplied it by \(5\) to find \(5d\). This gave us \(5d = 5(-6) = -30\).

By mastering these simple arithmetic operations, we can solve a range of mathematical problems, including more complex equations.