SAT Mathematics Practice Test 4

The expression $\left|\mathit{x}-1\right|-1$ will equal 0 if $\left|\mathit{x}-1\right|=1$. This is true for $\mathit{x}=2$ and for $\mathit{x}=0.$ For example, substituting $\mathit{x}=2$ into the expression $\left|\mathit{x}-1\right|-1$ and simplifying the result yields $\left|2-1\right|-1=|1|-1=1-1=0.$Therefore, there is a value of x for which $\left|\mathit{x}-1\right|-1$ is equal to 0.
Choice B is incorrect. By definition, the absolute value of any expression is a non-negative number. Substituting any value for x into the expression |x + 1| will yield a nonnegative number as the result. Because the sum ofa non-negative number and a positive number is positive, |x + 1| + 1 will be a positive number for any value of x. Therefore,$\left|\mathit{x}+1\right|+1\ne 0$ for any value of $\mathit{x}$. Choice C is incorrect. By definition, the absolute value of any expression is a non-negative number. Substituting any value for x into the expression $\left|1-\mathit{x}\right|$ will yield a non-negative number as the result. Because the sum of a non-negative number and a positive number is positive, $\left|1-\mathit{x}\right|+1$ will be a positive number for any value of x. Therefore,$\left|1-\mathit{x}\right|+1\ne 0$ for any value of $\mathit{x}$. Choice D is incorrect. By definition, the absolute value of any expression is a non-negative number. Substituting any value for x into the expression $\left|\mathit{x}-1\right|$ will yield a non-negative number as the result. Because the sum o1f a non-negative number and a positive number is positive,$\left|\mathit{x}-1\right|+$ will be a positive number for any value of x. Therefore, $\left|\mathit{x}-1\right|+1\ne 0$ for any value of $\mathit{x}$.