Video Transcript
Find the value of 𝑥 if two times
one minus three 𝑥 minus three plus six 𝑥 is equal to five minus seven 𝑥.
In this question, we are given an
equation involving an unknown value of 𝑥. And we are asked to use this
equation to determine the value of 𝑥. To do this, we can start by
recalling that in an equation, both sides of the equation are equal. So, we can apply the same
operations to both sides of the equation, and they will remain equal. We can use this to solve an
equation for an unknown by isolating the unknown on one side of the equation.
To isolate 𝑥, we need to collect
the like terms. So, we will start by distributing
over both sets of parentheses. We need to multiply each term
inside the parentheses by the factor outside. This gives us two minus six 𝑥
minus three minus six 𝑥 is equal to five minus seven 𝑥. We can combine the like terms on
the left-hand side of the equation to obtain negative one minus 12𝑥 is equal to
five minus seven 𝑥.
We now want to collect all of the
𝑥-terms on one side of the equation. To do this, we can add 12𝑥 to both
sides of the equation. However, this will leave us with a
constant term of five on the right-hand side of the equation. We can subtract five from both
sides of the equation to leave us with only 𝑥-terms on the right-hand side of the
equation. This gives us negative one minus
five is equal to negative seven 𝑥 plus 12𝑥.
We can simplify both sides of the
equation to get negative six equals five 𝑥. We can then divide both sides of
the equation through by five to obtain that 𝑥 is equal to negative six over
five. We can verify that this is the
value of 𝑥 by substituting this value into both sides of the given equation and
checking that they are equal. If we did this, we would see that
they are equal. And so 𝑥 equals negative six over
five is the value of 𝑥.
