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Solve x+14<25 . Make sure to write your inequality so that x comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparisons (<)
keyboard.

(1 point)

Solve x−8≥5
. Make sure to write your inequality so that x
comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
keyboard.

(1 point)

Solve x+10.5<20.2
. Make sure to write your inequality so that x
comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
keyboard.

(1 point)

Use the image to answer the question.

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.

What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x
comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
keyboard.

(1 point)

Question
Use the image to answer the question.



A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 1. A line is drawn from 1 toward 10 with an arrow at the end.
What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x
comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
keyboard.

(1 point)

1 answer

Let's solve each inequality step by step and ensure \(x\) comes first.

  1. Solve \(x + 14 < 25\): \[ x + 14 < 25 \] Subtract 14 from both sides: \[ x < 25 - 14 \] \[ x < 11 \] So the inequality is: \[ x < 11 \]

  2. Solve \(x - 8 \geq 5\): \[ x - 8 \geq 5 \] Add 8 to both sides: \[ x \geq 5 + 8 \] \[ x \geq 13 \] So the inequality is: \[ x \geq 13 \]

  3. Solve \(x + 10.5 < 20.2\): \[ x + 10.5 < 20.2 \] Subtract 10.5 from both sides: \[ x < 20.2 - 10.5 \] \[ x < 9.7 \] So the inequality is: \[ x < 9.7 \]

  4. Number line with open circle at 4 and line towards negative 10: This indicates that \(x\) is less than 4: \[ x < 4 \]

  5. Number line with closed circle at 1 and line towards 10: This indicates that \(x\) is greater than or equal to 1: \[ x \geq 1 \]

Now we have all the inequalities:

  1. \(x < 11\)
  2. \(x \geq 13\)
  3. \(x < 9.7\)
  4. \(x < 4\)
  5. \(x \geq 1\)