We want to solve the given equation.
The first step in solving the equation
is to simplify both sides of the equation
which means we clear the parentheses
by distributing and then combine like terms.
On the left side,
we distribute three to clear the parentheses.
On the right side,
we distribute four to clear the parentheses.
Three times six x is 18 x
and then three times negative two is negative six
giving us minus six and then we still have plus 11
equals on the right side four times five x is 20 x
and then four times negative five is negative 20
giving us minus 20 and then we still have plus three
and now we simplify both sides by combining like terms.
Notice on the left side we have two constant terms
and we also have two constant terms on the right.
So on the left, negative six plus 11 is positive five
and therefore the left side simplifies to 18 x plus five
equals on the right side negative 20 plus three
is negative 17.
The right side simplifies to 20 x minus 17.
The next step is to add or subtract
to isolate the variable terms on one side.
Notice right now we have 18 x on the left
and 20 x on the right.
To get the variable terms on one side,
we need to either subtract 20 x on both sides
or subtract 18 x on both sides.
Let's have the variable term be on the left
and therefore we will subtract 20 x on both sides.
Simplifying 18 x minus 20 x is a negative two x.
The left side simplifies to negative two x plus five.
On the right side, 20 x minus 20 x is zero
which is why we subtracted 20 x on both sides.
The right side is now just negative 17.
Again, we still have not isolated the variable term.
To isolate negative two x, we need to undo the plus five
by subtracting five on both sides.
Simplifying on the left, five minus five is zero
which is why we subtracted five on both sides.
The left side is now negative two x
equals on the right side negative 17
minus five is negative 22.
Now that we've isolated the variable term on the left side,
the next step is to multiply or divide
to isolate the variable.
Because negative two x means negative two times x,
to isolate x and undo the multiplication,
the next step is to divide both sides by negative two.
Simplifying negative two divided by negative two
simplifies to one.
One times x is x.
x equals on the right side
negative 22 divided by negative two is positive 11.
The solution is x equals 11
and let's go ahead and check our solution.
To check the solution,
we will now substitute 11 back into the original equation.
Performing the substitution gives us three
times the quantity six x minus two
would be six times 11 minus two and then we have plus 11
equals on the right side four times the quantity
five x minus five is five times 11 minus five
and then plus three.
Now, simplifying inside the parentheses, six times 11 is 66.
66 minus two is 64.
This gives us three times 64 plus 11
equals on the right side five times 11 is 55
minus five is 50 giving us four times 50 plus three.
Back on the left, three times 64 is 192.
We still have plus 11.
On the right side, four times 50 is 200
giving us 200 plus three.
192 plus 11 is 203 and 200 plus three is also 203
verifying the solution is correct.
I hope you found this helpful.