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# Inequalities: Overview

If \$\$x - 2 < 8\$\$ and \$\$x + 6 > 4\$\$, which of the following inequalities expresses all possible values of \$\$x\$\$?
Correct. [[Snippet]] Isolate \$\$x\$\$ in both inequalities. For \$\$x - 2 < 8\$\$, add \$\$2\$\$ to isolate \$\$x\$\$. >\$\$x - 2 + 2 < 8 + 2\$\$ >\$\$x < 10\$\$ For \$\$x + 6 > 4\$\$, subtract \$\$6\$\$ to isolate \$\$x\$\$. >\$\$x + 6 - 6 > 4 - 6\$\$ >\$\$x > -2\$\$ Based on this, \$\$x\$\$ must be greater than \$\$-2\$\$ and less than \$\$10\$\$. >\$\$-2 < x < 10\$\$
Incorrect. [[snippet]] Did you make a mistake when manipulating the second inequality? Subtract 6 from both sides of the inequality, as you would in an equation.
Incorrect. [[snippet]] Carefully check your work. Make sure you solve both inequalities for \$\$x\$\$.
Incorrect. [[snippet]] Carefully check your calculations. You need to solve both inequalities for \$\$x\$\$.
Incorrect. [[snippet]] Carefully check your calculations.
\$\$2 < x < 10\$\$
\$\$4 < x < 8\$\$
\$\$-2 < x < 10\$\$
\$\$-4 < x < 8\$\$
\$\$-8 < x < 4\$\$