Final answer:
To solve the equation 5|x+(3)/(4)|=10, divide both sides by 5 and consider two cases, where x+(3)/(4) is positive/zero and where it is negative. The solutions are x=5/(4) and x=-11/(4).
Step-by-step explanation:
To solve the equation 5|x+(3)/(4)|=10, we need to isolate the absolute value expression first. We can do this by dividing both sides of the equation by 5, leading to |x+(3)/(4)|=2. Now, we have two cases to consider:
- If x+(3)/(4) is positive or zero, then the absolute value has no effect and we can simply remove the absolute value bars. This leads to x+(3)/(4)=2. Solving this equation, we subtract (3)/(4) from both sides to get x=5/(4).
- If x+(3)/(4) is negative, then the absolute value will make it positive. In this case, we rewrite the equation as -(x+(3)/(4))=2. Expanding the negation, we get -x-(3)/(4)=2. We then subtract (3)/(4) from both sides and divide by -1 to solve for x, giving us x=-11/(4).
Therefore, the solutions to the equation are x=5/(4) and x=-11/(4).