Question

related questions: lesson 3: solving equations

what is the correct answer when you solve for a?

q. \\(0.48 = 2.4 - 1.6a\\)

a. \\(-5.2\\)
b. \\(-0.3\\)
c. \\(1.2\\)
d. \\(3.5\\)

Explanation:

Identify the given equation and target variable

We are given the linear equation:

$$ 0.48 = 2.4 - 1.6a $$

Our goal is to isolate and solve for the variable \(a\).

Isolate the variable term

Subtract \(2.4\) from both sides of the equation to isolate the term containing \(a\):

$$ 0.48 - 2.4 = -1.6a $$

Calculate the left side:

$$ -1.92 = -1.6a $$

Solve for the variable

Divide both sides by \(-1.6\) to solve for \(a\):

$$ a = \frac{-1.92}{-1.6} $$

Since both numbers are negative, the result is positive:

$$ a = \frac{1.92}{1.6} $$

Multiply the numerator and denominator by 100 to simplify the division:

$$ a = \frac{192}{160} $$

Simplify the fraction:

$$ a = 1.2 $$

Verify the solution

Substitute \(a = 1.2\) back into the original equation:

$$ 0.48 = 2.4 - 1.6(1.2) $$

Calculate the right side:

$$ 1.6 \times 1.2 = 1.92 $$

$$ 2.4 - 1.92 = 0.48 $$

The solution is correct and matches option C.

Answer:

• A. \(-5.2\)
• B. \(-0.3\)
• C. \(1.2\) (Correct answer)
• D. \(3.5\)