Find the value of 𝑥 when four 𝑥 plus five equals one plus five 𝑥.
Copying down this problem, we notice that we have a variable on both sides of our equation. In order to solve
this, we’ll need to get the 𝑥, the variable, onto one side of this equation.
The first step is
subtracting four 𝑥 from both sides of the equation. If I take four 𝑥 from a positive four 𝑥,
we’re left with zero. And if I take four 𝑥 from five 𝑥, I’m left with one 𝑥.
Now I need to bring
down the rest of our equation, and we have zero plus five equals one plus one 𝑥. Zero plus five
equals five. One plus one 𝑥 can be simplified to one plus 𝑥. Now I’m going to subtract one from
both sides of the equation. One minus one equals zero. Five minus one equals four.
We can bring
down the rest of our equation; bring down the 𝑥. Zero plus 𝑥 equals 𝑥, and that tells us that 𝑥
equals four. We can check our answer by plugging four back into our original equation. Four
times four equals 16 plus five; five times four equals 20; 21 equals 21, so our equation is true
when 𝑥 equals four.