How do you solve #-4/7x=6#?

Question

HIX Tutor · Accepted Answer

undefined To solve the equation -4/7x = 6, we need to isolate the variable x. Here are the steps:

1. Multiply both sides of the equation by the reciprocal of -4/7, which is -7/4. This will cancel out the fraction on the left side. 
   -4/7x * -7/4 = 6 * -7/4

2. Simplify the equation by multiplying:
   (4 * -4/7x) = -42/4

3. Simplify the left side further:
   -16/7x = -21/2

4. Divide both sides of the equation by -16/7 to solve for x:
   (-16/7x) / (-16/7) = (-21/2) / (-16/7)

5. Simplify the equation by dividing:
   x = 105/32

So the solution to -4/7x = 6 is x = 105/32.

Eli Assouline · Answer

#x = -21/2 = -10 1/2 = -10.5#

#-4/7x = 6#

#-4/7# is the only number we need to get rid of to be able to find #x#

The multiplicative inverse is the same as multiplying by its reciprocal.

#rarr# This will allow the entire number to cancel. #rarr# Remember to multiply by the same number on BOTH sides.

#color(red)(-7/4) xx -4/7x = color(red)(-7/4)xx 6#

#color(red)(-cancel7/cancel4) xx -cancel4/cancel7x = color(red)(-7/cancel4^2)xx cancel6^3 " " (-xx- =+)#

#x = -21/2 = -10 1/2 = -10.5#

Avery Alexander · Answer

undefined To solve the equation $-\frac{4}{7}x = 6$, you can isolate $x$ by multiplying both sides of the equation by the reciprocal of $-\frac{4}{7}$, which is $-\frac{7}{4}$.

$$
\begin{align*}
-\frac{4}{7}x &= 6 \
-\frac{7}{4} \cdot \left(-\frac{4}{7}x\right) &= -\frac{7}{4} \cdot 6 \
x &= -\frac{7}{4} \cdot 6 \
x &= -\frac{42}{4} \
x &= -10.5
\end{align*}
$$

So, the solution to the equation is $x = -10.5$.