Solve the following equation for $x$.
$10=2-4(a x-3)$
A. $-\frac{5}{a}$
B. $\frac{1}{a}$
C. $\frac{5}{a}$
D. $-\frac{1}{a}$
Answer (1)
Expand the equation: 10 = 2 − 4 a x + 12 .
Combine constants: 10 = 14 − 4 a x .
Isolate the term with x : − 4 = − 4 a x .
Solve for x : x = a 1 .
The correct answer is a 1 .
Explanation
Understanding the Problem We are given the equation 10 = 2 − 4 ( a x − 3 ) and we need to solve for x . Our goal is to isolate x on one side of the equation.
Expanding the Equation First, we expand the equation by distributing the − 4 into the parentheses: 10 = 2 − 4 a x + 12
Combining Constants Next, we combine the constants on the right side of the equation: 10 = 14 − 4 a x
Isolating the x Term Now, we want to isolate the term with x . We subtract 14 from both sides of the equation: 10 − 14 = 14 − 4 a x − 14
− 4 = − 4 a x
Solving for x To solve for x , we divide both sides by − 4 a : − 4 a − 4 = − 4 a − 4 a x
a 1 = x
Final Answer Therefore, the solution for x is a 1 . Comparing this to the given options, we see that it matches option B.
Examples
Understanding how to solve linear equations is crucial in many real-world scenarios. For instance, imagine you are a sales manager and need to determine the number of products to sell to reach a specific revenue target. By setting up a linear equation with the number of products as the variable, you can solve for the exact quantity needed to meet your goal. This skill is also applicable in budgeting, financial planning, and even in everyday tasks like calculating the cost of items with discounts.
