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Solve the Inequality for x

4x − 5 ≥ 7  

Move all terms not containing x to the right side of the inequality.

4x ≥ 12

Divide each term by 4 and simplify.

x ≥ 3

The result can be shown in multiple forms.

Inequality Form:

x ≥ 3

Interval Notation:

[3,∞)

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You graph it here

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Answer:

Step-by-step explanation:

Alright, so this is basically just another equation, but then you see the greater than or equal to sign. How do I solve this? You may be asking. Well, treat it like an equation and worry about the sign later.

4x - 5 [tex]\geq[/tex] 7

Solve for x.

Add 5 to each side, then divide by 4 to each side.

4x [tex]\geq[/tex] 12

x [tex]\geq[/tex] 3  <----This is the answer.

Now for the graph. Look at the picture below:

That's what the graph should look like. Since it has a greater than or equal to sign, the line will be solid.

The graph is basically saying that anything that is greater than 3 (including 3) is counted, which is why that entire right side of 3 is shaded in.

Also, the way you should technically graph it is on a number line. So make a number line.

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

<-----|-----|-----|-----|-----|-----€-----|-----|-----|-----|-----|-----|-----|----->

(Pretend € is the filled in dot).

So, the above number line is what it should look like when graphed. The € circle is filled in because we are including the 3.

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