Question

solve each inequality and graph its solution.

1. $-11 \geq 6 - 2n - 5$

1. $x + 1 + 4 \leq 9$

Explanation:

Step1: Simplify right-hand side

$-11 \geq 6 - 5 - 2n$
$-11 \geq 1 - 2n$

Step2: Subtract 1 from both sides

$-11 - 1 \geq -2n$
$-12 \geq -2n$

Step3: Divide by -2, reverse inequality

$\frac{-12}{-2} \leq \frac{-2n}{-2}$
$6 \leq n$ or $n \geq 6$

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Step1: Simplify left-hand side

$x + (1+4) \leq 9$
$x + 5 \leq 9$

Step2: Subtract 5 from both sides

$x \leq 9 - 5$
$x \leq 4$

Answer:

1. The solution is $n \geq 6$. To graph this: Draw a closed dot at 6 on the number line, then shade all values to the right (towards 7, 8, ..., 11).
2. The solution is $x \leq 4$. To graph this: Draw a closed dot at 4 on the number line, then shade all values to the left (towards 3, 2, 1, ...).