Problem 74 - Algebra 2

Question

PREREQUISITE SKILL Evaluate each expression if \(a=2, b=-\frac{3}{4},\) and \(c=1.8 .(\text { lesson } 1-1)\) $$ 1.5 c-7 $$

Step-by-Step Solution

Answer

The value of the expression is -4.3.

Step 1: Substitute the Given Values

The expression given for evaluation is \(1.5c - 7\). We need to substitute the provided value of \(c=1.8\) into the expression. After substitution, the expression becomes \(1.5 \times 1.8 - 7\).

Step 2: Calculate the Multiplication

Perform the multiplication \(1.5 \times 1.8\). Calculate: \(1.5 \times 1.8 = 2.7\).

Step 3: Perform the Subtraction

Now, substitute \(2.7\) into the expression from Step 1 to get \(2.7 - 7\). Calculate: \(2.7 - 7 = -4.3\).

Step 4: Confirm the Evaluation

The final evaluation of the expression is \(-4.3\). Ensure all calculations are correct by verifying each step.

Key Concepts

Substitution

Substitution in algebra involves replacing a variable with a known value in an expression. This step is crucial as it changes the expression from one involving variables to a numerical one that can be simplified. In the original exercise, the expression is given as \(1.5c - 7\). We substitute \(c\) with the value \(1.8\) because that's what is provided. It's important to always carefully substitute the value and ensure that each variable is replaced correctly. For example:

• Given \(c = 1.8\), the expression becomes \(1.5 \times 1.8 - 7\).

This step sets the stage for further calculations, like multiplication and subtraction, so it's vital to do it right.

Multiplication

Multiplication is one of the fundamental operations in arithmetic and involves the process of scaling one quantity by another. In the context of the original exercise, after substituting \(c\) with \(1.8\), we now have the task of calculating \(1.5 \times 1.8\). When performing multiplication, it may help to break down the numbers into simpler components, especially if you're doing it by hand:

• \(1.5\) can be thought of as \(1 + 0.5\).
• Multiply \(1 \times 1.8\) to get \(1.8\).
• Multiply \(0.5 \times 1.8\) to get \(0.9\).
• Add the results: \(1.8 + 0.9 = 2.7\).

This process confirms that \(1.5 \times 1.8 = 2.7\), setting us up for the next step.

Subtraction

Subtraction is the process of deducting one number from another, which in this context helps us simplify and further solve the expression. Following the multiplication in the original exercise, we now substitute \(2.7\) back into the expression, resulting in \(2.7 - 7\). To perform this subtraction:

• Consider \(2.7\) as a number on the number line.
• Subtracting \(7\) means moving left on the number line.
• If you start at \(2.7\) and move left by \(7\), you cross \(zero\) and continue to \(-4.3\).

This calculation gives us the result of the subtraction step, which is \(-4.3\.\), finishing the expression simplification.

Evaluation

Evaluation involves simplifying an expression to arrive at a numerical answer. It's the final step where we confirm that all previous steps—substitution, multiplication, and subtraction—were done accurately. In solving the original exercise's expression, we reach the final result of \(-4.3\). To ensure the evaluation is correct, check:

• Each substitution was executed as per the given values.
• Multiplication calculations were double-checked for accuracy.
• The subtraction operation was performed correctly.

Going through these checks makes sure that the expression evaluation is accurate. Thus, the expression \(1.5c - 7\) with \(c = 1.8\) accurately evaluates to \(-4.3\.\)