Video Transcript
Given that two times the absolute value of negative 12 is equal to two times the absolute value of 𝑥 plus one, find the value of 𝑥.
When you first look at this expression, you might want to calculate the absolute value of negative 12, which is 12, so that the left side of the equation is two times 12. From there, you could multiply two times 12 to get 24. And remember, our goal is to find 𝑥. So we need to try to isolate 𝑥. So we divide both sides of the equation by two. And we get that 12 is equal to the absolute value of 𝑥 plus one.
But let’s look at a different method for simplifying this expression. Since we’re multiplying by two on both sides of this equation, for our first step, we could’ve divided by two on both sides of the equation. And then we would immediately have the absolute value of negative 12 is equal to the absolute value of 𝑥 plus one. 12 equals the absolute value of 𝑥 plus one.
And we know when we’re solving absolute value equations, we need to consider two cases: the positive case 12 equals 𝑥 plus one and the negative case 12 equals the negative of 𝑥 plus one. For equation on the left, we simply solve by subtracting one from both sides, which gives us 11 is equal to 𝑥. For the equation on the right, we can multiply through by negative one, which will give us negative 12 is equal to 𝑥 plus one. And then to solve, we subtract one from both sides, which gives negative 13 is equal to 𝑥.
The solutions for 𝑥 here will be 11 or negative 13.
