How do you solve #x/3=-10#?

2 Answers
Jun 14, 2018

Answer:

#x = -30#

Explanation:

When dealing with equalities, you can multiply both sides by a same number, and the inequality will preserve its truth value. By this, I mean that if you start with a true equality, it will still be true, for example

#3 = 3 \to 3*4 = 3*4 \to 12=12#

So, we started with a true equality (#3=3#), and we multiplied both sides by #4#, obtaining another true identity (#12=12#).

On the other hand, if the two sides are different, they will still differ after being multiplied by the same number:

#3 \ne 2 \to 3*6 \ne 2*6 \to 18 \ne 12#

So, we started with a false equality (#3\ne 2#), and we multiplied both sides by #6#, obtaining another true identity (#18 \ne 12#).

In your case, you only need to multiply both sides by #3#: the expression becomes

#3*\frac{x}{3} = -10*3#

Why did we choose #3#? Because our goals is to isolate the #x# on the left side, obtaining an expression like #x=...#. And the #3# we multiplied by simplifies with the #3# at the denominator, allowing us to reach our goal:

#cancel(3)*\frac{x}{cancel(3)} = -10*3#

Of, course, this comes with the price of an added calculation on the right hand side, but that's not much of a problem:

#x = -10*3 = -30#

Equation solved! In fact, we reached a form like #x=k#, for some real number #k#, which means that that particular value is the solution for the equation.

Jun 14, 2018

Answer:

#x=-30#

Explanation:

Given: #x/3=-10#

The objective is to end up with just one #x# and for it to be on its own on one side of the = and everything else on the other side.

To end up with just #x# on the left we change the #1/3# into 1. This is because #1xx x# is just #x#

#color(green)(x/3=-10 color(white)("dddd") ->color(white)("dddd") x xx1/3=-10#

Multiply both sides by #color(red)(3)#

#color(green)( color(white)("dddddddddddd") ->color(white)("dddd") x xx1/3color(red)(xx3)=-10color(red)(xx3)#

#color(green)( color(white)("dddddddddddd") ->color(white)("dddd") x color(white)("dd")xx3/3color(white)(".d")=-30)#

But #3/3# is the same value as 1 giving: #color(white)("dd")x=-30#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("General shortcut rule")#

To move a value to the other side of the equals:

For addition or subtraction:
# color(white)("dd")#Move to the other side and apply the opposite action. Addition is # color(white)("dd")#changed to subtraction and subtraction is changed to addition.

For division or subtraction:
#color(white)("dd")#Move to the other side and apply the opposite action. Division is #color(white)("dd")#changed to multiplication and multiplication is changed to
#color(white)(".d")# division.