Question

Solve for x and graph the solution on the number line below.
- 4x – 2 < -6 and - 4x – 2 > -42

Answer 1

The solution to the system of inequality expression is 1 < x < 10

Inequality expressions are expressions not separated by an equal sign

Given the inequality expressions

- 4x – 2 < -6 and - 4x – 2 > -42

For the inequality - 4x – 2 < -6

- 4x – 2 + 2 < -6 + 2

-4x < -4

x > 1

For the inequality  - 4x – 2 > -42

- 4x – 2 + 2> -42 +2

-4x > -40

x < 10

Combining both inequality solutions:

1 < x < 10

Hence the solution to the system of inequality expression is 1 < x < 10

Representing on the number line we have:

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Answer 2

The general solution of the pair of equations:

- 4x – 2 < -6 and - 4x – 2 > -42 is; 1 < x > 10

By solving the first inequality;

• -4x - 2 < -6

• -4x < -4

By dividing both sides by -4, we have;

x > 1

Subsequently, by solving the second inequality;

• - 4x – 2 > -42
• -4x > -40

By dividing both sides by -4, we have;

x < 10

Therefore, the inequality that satisfies both equations is;

1 < x > 10

The image attached contains the solution on the number line.

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