Solve and check the linear equation.
-$$0.24 ( 70 ) + 0.40 x = 0.30 ( 70 + x )$$
A) $\{ 40 \}$
B) $\{ 30 \}$
C) $\{ 50 \}$
D) $\{ 20 \}$

Question

Quizplus · Accepted Answer

First, distribute the numbers: $0.24 \times 70 + 0.40x = 0.30 \times 70 + 0.30x$. This simplifies to $16.8 + 0.40x = 21 + 0.30x$. Subtract $0.30x$ from both sides to get $0.10x = 4.2$. Dividing both sides by $0.10$ gives $x = 42$. However, none of the options match this result, indicating a mistake in my calculation. Let's correct the process:Starting again with the equation: $0.24(70) + 0.40x = 0.30(70 + x)$.First, simplify inside the parentheses: $16.8 + 0.40x = 21 + 0.30x$.Subtract $16.8$ from both sides: $0.40x = 4.2 + 0.30x$.Subtract $0.30x$ from both sides: $0.10x = 4.2$.Divide both sides by $0.10$: $x = 42$.Given the mistake in matching the result with the provided options and the correct calculation process, it seems there was an error in my initial explanation. The correct approach to solve the equation is as follows, but please note the initial result and options provided do not align correctly with standard solution steps. The correct solution process should involve correctly distributing, combining like terms, and solving for $x$, but the final answer should match one of the provided options, which was not correctly identified in my initial response.

Solve and Check the Linear Equation 0.24(70)+0.40x=0.30(70+x)0.24 ( 70 ) + 0.40 x = 0.30 ( 70 + x )0.24(70)+0.40x=0.30(70+x)

Solve and Check the Linear Equation $0.24 ( 70 ) + 0.40 x = 0.30 ( 70 + x )$