Solve the linear equation:
[tex]$3.4+2(9.7-4.8 x)=61.2$
What are the possible steps involved in solving this equation? Check all that apply.
A. Add 3.4 and 2.
B. Distribute 2 to 9.7 and [tex]$-4.8 x$.
C. Combine 3.4 and 19.4.
D. Divide both sides by 22.8.
E. Subtract 22.8 from both sides.
F. Divide both sides by -9.6.
Answer (2)
Distribute 2 to the terms inside the parenthesis: 2 ( 9.7 − 4.8 x ) = 19.4 − 9.6 x .
Combine the constant terms: 3.4 + 19.4 = 22.8 , resulting in the equation 22.8 − 9.6 x = 61.2 .
Subtract 22.8 from both sides: − 9.6 x = 38.4 .
Divide both sides by -9.6 to solve for x: x = − 9.6 38.4 = − 4 . The final answer is − 4 .
Explanation
Understanding the Equation We are given the equation 3.4 + 2 ( 9.7 − 4.8 x ) = 61.2 and we want to solve for x . Let's break down the steps to isolate x and find its value.
Distributing the Constant First, we need to distribute the 2 inside the parentheses: 2 ( 9.7 − 4.8 x ) = 2 × 9.7 − 2 × 4.8 x = 19.4 − 9.6 x
Substituting Back Now, substitute this back into the original equation: 3.4 + 19.4 − 9.6 x = 61.2
Combining Constants Combine the constant terms on the left side of the equation: 3.4 + 19.4 = 22.8 So the equation becomes: 22.8 − 9.6 x = 61.2
Isolating the x Term Next, we want to isolate the term with x . Subtract 22.8 from both sides of the equation: 22.8 − 9.6 x − 22.8 = 61.2 − 22.8 − 9.6 x = 38.4
Solving for x Finally, divide both sides by -9.6 to solve for x :
x = − 9.6 38.4 = − 4
Examples
Linear equations are used in everyday life to calculate costs, plan budgets, or determine distances. For example, if you are planning a road trip and know the average speed you'll be driving and the distance you need to travel, you can use a linear equation to determine how long the trip will take. Similarly, if you are buying items at a store and have a coupon, you can use a linear equation to calculate the final cost after the discount.
To solve the equation 3.4 + 2 ( 9.7 − 4.8 x ) = 61.2 , we first distribute, combine like terms, isolate x , and finally divide to find that x = − 4 . The correct steps involved in solving the equation include distributing the 2, combining constants, and isolating x . Therefore, the right steps to check are B, C, E, and F.
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