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How do you solve and graph #x-1<=5# or #x+3>=10# ?

Answer 1

Nathan Axel

Solved: #x <= 6 # union with #x >= 7#

For the inequality: #x -1 <= 5 # add a 1 to both sides to get #x <= 6 #

For the inequality: #x +3 >= 10 # subtract a 3 from both sides to get #x >= 7#

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Answer 2

Eva Abramson

To solve the inequality (x - 1 \leq 5) or (x + 3 \geq 10), we first solve each inequality separately and then combine the solutions.

For the inequality (x - 1 \leq 5): [ \begin{align*} x - 1 & \leq 5 \ x & \leq 6 \end{align*} ]

For the inequality (x + 3 \geq 10): [ \begin{align*} x + 3 & \geq 10 \ x & \geq 7 \end{align*} ]

Combining the solutions, we have (x \leq 6) or (x \geq 7).

Graphically, this represents two separate intervals on the number line: ((-\infty, 6]) and ([7, +\infty)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and graph #x-1&lt;=5# or #x+3&gt;=10# ?

How do you solve and graph #x-1<=5# or #x+3>=10# ?