Solve for xx and graph the solution on the number line below.

Question

minus, 1, is greater than, start fraction, x, divided by, minus, 4, end fraction
−1>
−4
x
​

Answer
Attempt 1 out of 3


Inequality Notation:
Number Line:
Click and drag to plot line.
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
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Answer 1

To solve the inequality, we need to isolate x on one side of the inequality symbol.

We have the inequality: −1 > (x/-4)

To isolate x, we can multiply both sides of the inequality by -4. However, when we multiply or divide an inequality by a negative number, we need to reverse the direction of the inequality.

So, multiplying both sides by -4, we have:
-4*(-1) < x
4 < x

Inequality Notation: 4 < x

Now, let's graph this solution on the number line:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

We plot a closed circle at 4, since the inequality is strict (4 is not included in the solution). Then, we shade to the right of 4 to represent all values greater than 4.

Number Line:
----------------------●-------------------->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

So, the solution is x > 4, which means x is any value greater than 4.