Solve the following equations.(A) 2∣x∣=102\left|x\right|=10

x = { 5 , − 5 } x=\left\lbrace5,-5\right\rbrace x = { 5 , − 5 }

Solve the following equations. ( A ) 2 ∣ x ∣ = 10 2\left|x\right|=10

Welcome to the practice. In this problem, we'd like to solve the equation two times the absolute value of x equals 10. We know that the first step of solving any absolute value equation is to isolate the absolute value on one side of the equation, but we can see in our equation that we don't have the absolute value all by itself. We have two times the absolute value of x. So the first thing we have to do is get rid of this two here, which we can do by dividing both sides of the equation by two. It will get rid of the two as we want on the left, leaving us with absolute value of x, and on the right, we get 10 divided by two, which is five. So now we have absolute value of something equals positive number, and we know that we can break that up up into our two equations without absolute value, where the first one is the thing inside the absolute value x equal to our a value, which in this case is five, and the second takes x and sets it equal to negative a, which in this case is negative five. We can see that neither of these two equations needs extra work to solve, so our solutions are x equals five and x equals negative five. But feel free to take both of these values and plug them in for x back into the original equation, and you'll see that you do get a true statement. So the solution set for this equation includes five and negative five. Great work.