Question

3Multiple Choice Solve \(3 h-5=13\). (Algebra Revieto) \(\begin{array}{llll}\text { (A) }-4 & \text { (B) }-2 & \text { (C) }-7 & \text { (D) } 6\end{array}\)

Short answer

The solution is \( h = 6 \), which corresponds to option (D).

Step-by-step solution

Identify the Equation

Recognize the given algebraic equation to solve, which is: \(3h - 5 = 13\).

Isolate the Variable Term

Add 5 to both sides of the equation to eliminate the constant on the left side: \(3h - 5 + 5 = 13 + 5\). This simplifies to \(3h = 18\).

Solve for the Variable

Divide both sides by 3 to solve for \(h\): \(\frac{3h}{3} = \frac{18}{3}\). Simplifying gives \(h = 6\).

Verify the Solution

Substitute \(h = 6\) back into the original equation to check: \(3(6) - 5 = 13\). Calculate: \(18 - 5 = 13\), confirming that the solution is correct.

Choose the Correct Option

Identify the correct option from the given choices. The solution \(h = 6\) corresponds to option (D).

Key concepts

Solving Equations

When it comes to solving equations, the primary goal is to find the value of the unknown variable that makes the equation true. An equation is a mathematical statement that asserts the equality of two expressions, each usually on either side of an equals sign. To solve an equation, follow these steps:

• First, understand what the equation is asking. In the case of our example, the equation is \(3h - 5 = 13\).
• Next, identify operations affecting the variable and perform inverse operations to isolate the variable.
• Finally, continue simplifying until the variable is on one side of the equation and the answer is clear.

Breaking down problems into these steps makes complicated problems much simpler and easier to handle.

Variables

Variables are symbols used to represent numbers in equations and algebraic expressions. In algebra, variables are usually denoted by letters like \(h\), \(x\), \(y\), etc. They allow us to work with unknown values and develop general formulae.

• A variable, such as the \(h\) in our equation, acts as a placeholder for a number we need to find.
• When we 'solve for a variable,' we are determining what value, when substituted for the variable, makes the equation true.
• Understanding the role of variables allows students to transition from arithmetic to algebra, where they solve for unknowns.

Determining the value of variables is a fundamental aspect of algebra and will be used in a wide array of mathematical applications.

Equation Balancing

Equation balancing is crucial because it ensures equality is maintained. This principle states that whatever operation you perform on one side of the equation, you must do the same on the other side. This keeps the equation balanced like a scale.

• If you add a number to one side, add the same number to the other side.
• If you divide one side by a certain number, divide the other side by the same number.
• Through balancing, the steps you take to solve the equation do not alter its core equality.

In our example, by adding 5 to both sides of the equation \(3h - 5 = 13\), and then dividing both sides by 3, we find \(h = 6\), all while keeping the equation balanced. Adhering to these core principles helps in accurately solving for the variable.