Problemas
Solve the inequality. Graph the solution. (1)/(12)vert 2x-5vert +11leqslant 12 Select the correct choice below and, if necessary.fill in the answer boxes to complete your choice. A. square leqslant xleqslant square B. xleqslant square or xgeqslant square C. The solution is all real numbers. D. There is no solution.
Solución
Zósimomaestro · Tutor durante 5 años
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To solve the inequality, we first isolate the absolute value expression:<br /><br />$\frac {1}{12}\vert 2x-5\vert +11\leqslant 12$<br /><br />Subtract 11 from both sides:<br /><br />$\frac {1}{12}\vert 2x-5\vert \leqslant 1$<br /><br />Multiply both sides by 12:<br /><br />$\vert 2x-5\vert \leqslant 12$<br /><br />This inequality means that the expression inside the absolute value, $2x-5$, is between -12 and 12. We can split this into two separate inequalities:<br /><br />$-12 \leqslant 2x-5 \leqslant 12$<br /><br />Now, we solve each inequality separately:<br /><br />For the left inequality:<br />$-12 \leqslant 2x-5$<br />Add 5 to both sides:<br />$-7 \leqslant 2x$<br />Divide both sides by 2:<br />$-3.5 \leqslant x$<br /><br />For the right inequality:<br />$2x-5 \leqslant 12$<br />Add 5 to both sides:<br />$2x \leqslant 17$<br />Divide both sides by 2:<br />$x \leqslant 8.5$<br /><br />Combining the solutions, we have:<br />$-3.5 \leqslant x \leqslant 8.5$<br /><br />Therefore, the correct choice is A. $-3.5 \leqslant x \leqslant 8.5$.
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