Question

Which number line represents the solution to the inequality −7x − 13 ≥ 8?

Answer 1

Answer:

$x \leq -3$

Kindly refer to the attached image for answer.

Step-by-step explanation:

Given the equation:

$-7x - 13 \geq 8$

First of all, let us simplify the given inequality:

Adding 13 to both sides, there will be no effect on the inequality:

$-7x-13+13\geq 8+13\\\Rightarrow -7x\geq21$

Now, dividing by 7 which is a positive integer, so there will be no effect on the inequality:

$-x\geq 3$

Now, multiplying with -1, the inequality will get changed.

Greater than equal to will be changed to Less than equal to.

So, now, the inequality becomes:

$x \leq -3$

Plotting it on the number line, it will contain number -3 and numbers less than -3.

Kindly refer to the attached image.

Answer 2

The solution to the system of inequality x ≤ - 3

Inequality functions

Given the inequality expression −7x − 13 ≥ 8

Add 13 to both sides of the equation

−7x − 13 + 13 ≥ 8 + 13

-7x  ≥ 8 + 13

-7x  ≥ 21

Divide both sides by -7

-7x/-7  ≤ 21/-7

x ≤ - 3

Hence the solution to the system of inequality x ≤ - 3

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