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Video: Solving Linear Equations with an Unknown on Both Sides of the Equation

Kathryn Kingham

Find the value of 𝑥: 4𝑥 + 5 = 1 + 5𝑥.

01:59

Video Transcript

Find the value of π‘₯ when four π‘₯ plus five equals one plus five π‘₯.

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 π‘₯, the variable, onto one side of this equation.

The first step is subtracting four π‘₯ from both sides of the equation. If I take four π‘₯ from a positive four π‘₯, we’re left with zero. And if I take four π‘₯ from five π‘₯, I’m left with one π‘₯.

Now I need to bring down the rest of our equation, and we have zero plus five equals one plus one π‘₯. Zero plus five equals five. One plus one π‘₯ can be simplified to one plus π‘₯. 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 π‘₯. Zero plus π‘₯ equals π‘₯, and that tells us that π‘₯ 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 π‘₯ equals four.