Video Transcript
Find the value of 𝑥 if eight 𝑥 plus two is equal to six minus two 𝑥.
In this question, we are given an equation involving an unknown value of 𝑥 and we
need to use this equation to determine the value of 𝑥. To do this, we can start by recalling that we need to rearrange the equation to
isolate 𝑥 on one side of the equation. We should start by collecting the like terms on the same side of the equation. To do this, we need to add two 𝑥 to both sides of the equation. On the left-hand side of the equation, we can add eight 𝑥 to two 𝑥 to obtain
10𝑥. And on the right-hand side of the equation, we have negative two 𝑥 plus two 𝑥
equals zero.
Now that the 𝑥-terms are combined, we want to isolate 𝑥. We can subtract two from both sides of the equation and evaluate to get 10𝑥 equals
four. We can now isolate 𝑥 on the left-hand side of the equation by dividing both sides of
the equation by 10. We obtain that 𝑥 equals four over 10. We can cancel the shared factor of two in the numerator and denominator to get that
𝑥 equals two-fifths.
We can verify that this is the solution to the equation by substituting this value
into the equation and verifying that both sides of the equation are equal. If we do this, then we can verify that 𝑥 is equal to two over five.
