Solve the compound inequality. Express the answer in interval notation.
(B) $2 x minus 3 is less than or equal to 1$ or $- x + 4 \leq 10$

$(- \infty, - 14] \cup [- 1, \infty)$

$open bracket negative 6 comma 2 close bracket$

$(- \infty, - 6] \cup [2, \infty)$

$(- \infty, \infty)$

Verified step by step guidance

Identify the two inequalities given in the compound inequality: $2x - 3 \leq 1$ and $-x + 4 \leq 10$.

Solve the first inequality $2x - 3 \leq 1$ by isolating $x$: add 3 to both sides to get $2x \leq 4$, then divide both sides by 2 to find $x \leq 2$.

Solve the second inequality $-x + 4 \leq 10$ by isolating $x$: subtract 4 from both sides to get $-x \leq 6$, then multiply both sides by $-1$ (remember to reverse the inequality sign) to get $x \geq -6$.

Since the compound inequality uses "or", the solution is all values of $x$ that satisfy either $x \leq 2$ or $x \geq -6$.

Combine the solution sets: $x \leq 2$ includes all numbers less than or equal to 2, and $x \geq -6$ includes all numbers greater than or equal to -6. Together, these cover all real numbers, so the solution in interval notation is $(-\infty, \infty)$.

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Solve the compound inequality. Express the answer in interval notation.(B) 2x−3≤12x-3\(\le\)1 or −x+4≤10-x+4\(\le\)10

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Solve the compound inequality. Express the answer in interval notation.
(B) $2 x minus 3 is less than or equal to 1$ or $- x + 4 \leq 10$