Question

Solve. 3/4x+1/4=−1/2x−3 Responses x=−11/5 x equals negative fraction 11 over 5 x=−13/5 x equals negative fraction 13 over 5 x=−13

Answer 1

Answer:

$-\dfrac{13}{5}$

Step-by-step explanation:

Let's solve the equation:

$\dfrac{3}{4}x + \dfrac{1}{4} = -\dfrac{1}{2}x - 3$

Add $\dfrac{1}{2}x$ and subtract $\dfrac{1}{4}$ on both sides.

$\dfrac{3}{4}x +\dfrac{1}{4}+ \dfrac{1}{2}x -\dfrac{1}{4} =-\dfrac{1}{2}x -3 +\dfrac{1}{2}x - \dfrac{1}{4}$

$\dfrac{3}{4}x + \dfrac{1}{2}x = -3 - \dfrac{1}{4}$

Now, find a common denominator for the fractions on the left side:

$\dfrac{6}{8}x + \dfrac{4}{8}x = -3 - \dfrac{1}{4}$

Combine the terms on the left side:

$\dfrac{10}{8}x = -\dfrac{13}{4}$

Reduce the fraction on both sides:

$\dfrac{5}{4}x = -\dfrac{13}{4}$

Now, isolate x by multiplying both sides by the reciprocal of the coefficient of x:

$x = -\dfrac{13}{4} \times \dfrac{4}{5}$

Simplify:

$\Large\boxed{\boxed{x = -\dfrac{13}{5}}}$

So, the correct solution is $x = -\dfrac{13}{5}$. Therefore, the option "x equals negative fraction 13 over 5" is the correct response.

Answer 2

Answer:

$x=-\dfrac{13}{5}$

Step-by-step explanation:

Given equation:

$\dfrac{3}{4}x+\dfrac{1}{4}=-\dfrac{1}{2}x-3$

To solve the equation for x, begin by expressing the coefficients and constants as fractions with the common denominator of 4:

$\dfrac{3}{4}x+\dfrac{1}{4}=-\dfrac{2}{4}x-\dfrac{12}{4}$

Next, add 2x/4 to both sides of the equation:

$\dfrac{3}{4}x+\dfrac{1}{4}+\dfrac{2}{4}x=-\dfrac{2}{4}x-\dfrac{12}{4}+\dfrac{2}{4}x$

$\dfrac{3}{4}x+\dfrac{2}{4}x+\dfrac{1}{4}=-\dfrac{12}{4}$

Now subtract 1/4 from both sides:

$\dfrac{3}{4}x+\dfrac{2}{4}x+\dfrac{1}{4}-\dfrac{1}{4}=-\dfrac{12}{4}-\dfrac{1}{4}$

$\dfrac{3}{4}x+\dfrac{2}{4}x=-\dfrac{12}{4}-\dfrac{1}{4}$

Combine like terms:

$\dfrac{5}{4}x=-\dfrac{13}{4}$

Multiply both sides of the equation by 4/5:

$\dfrac{5}{4}x\cdot \dfrac{4}{5}=-\dfrac{13}{4}\cdot \dfrac{4}{5}$

Cross-cancel the common factors:

$\dfrac{\diagup\!\!\!\!5}{\diagup\!\!\!\!4}x\cdot \dfrac{\diagup\!\!\!\!4}{\diagup\!\!\!\!5}=-\dfrac{13}{\diagup\!\!\!\!4}\cdot \dfrac{\diagup\!\!\!\!4}{5}$

$x=-\dfrac{13}{5}$

Therefore, the solution to the given equation is:

$\Large\boxed{\boxed{x=-\dfrac{13}{5}}}$