Solve the inequality and graph the solution on the line provided.

Question

2, x, minus, 2, is less than, 0
2x−2<
0
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 1

To solve the inequality \( 2x - 2 < 0 \):

1. Isolate \( x \): \[ 2x - 2 < 0 \] Add 2 to both sides: \[ 2x < 2 \] Now divide both sides by 2: \[ x < 1 \]

Now, the solution in inequality notation is: \[ x < 1 \]

2. Graphing the Solution: On the number line, you would represent the solution \( x < 1 \) by placing an open circle at 1 to indicate that 1 is not included in the solution, and shading the line to the left of 1 to indicate all numbers less than 1 are included in the solution.

Here’s how you would represent it:

<----(----------)---->
      0          1

• The open parenthesis ( indicates that 1 is not included in the solution.
• The shading to the left indicates all numbers less than 1 are included.

Answer 2

Solve the inequality and graph the solution on the line provided.
minus, 70, minus, 6, x, is less than or equal to, minus, 112
−70−6x≤
−112
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 3

To solve the inequality \( -70 - 6x \leq -112 \):

1. Isolate \( x \): First, add 70 to both sides of the inequality: \[ -6x \leq -112 + 70 \] Simplifying the right-hand side: \[ -6x \leq -42 \]

2. Divide by -6: When dividing or multiplying both sides of an inequality by a negative number, you must flip the inequality sign: \[ x \geq \frac{-42}{-6} \] Simplifying: \[ x \geq 7 \]

Now the solution in inequality notation is: \[ x \geq 7 \]

3. Graphing the Solution: On the number line, you would represent the solution \( x \geq 7 \) by placing a closed circle at 7 to indicate that 7 is included in the solution, and shading the line to the right of 7 to indicate all numbers greater than or equal to 7 are included in the solution.

Here’s how you would represent it:

<----[----------)---->
      6          7

• The square bracket [ indicates that 7 is included in the solution.
• The shading to the right indicates all numbers greater than or equal to 7 are included.