How do I solve and graph

3¡Ý 2x-4

Also this one
2(x-3)> 5x-14

To solve and graph equations or inequalities, you can follow these steps:

1. Solve the equation or inequality to find the value(s) of the variable.
2. Represent the solution on a number line.
3. If necessary, graph the solution on the coordinate plane.

Let's apply these steps to solve and graph the given equations:

1. 3 ≥ 2x - 4:

To solve this inequality, we need to isolate the variable (x) on one side of the inequality sign (≥).

First, add 4 to both sides of the inequality:
3 + 4 ≥ 2x - 4 + 4

Simplifying, we get:
7 ≥ 2x

Next, divide both sides of the inequality by 2 (the coefficient of x):
7/2 ≥ 2x/2

Simplifying further, we have:
7/2 ≥ x

So, the solution for the inequality is x ≤ 7/2.

2. To represent this solution on a number line, draw a horizontal line with an arrow pointing to the left side, indicating that x can take any value less than or equal to 7/2.

3. There is no need to graph this solution on a coordinate plane since it is a one-dimensional line.

Now let's solve the second equation:

2(x - 3) > 5x - 14:

Apply the distributive property by multiplying 2 with each term inside the parentheses:
2x - 6 > 5x - 14

Next, we need to isolate the x term on one side of the inequality. To do this, subtract 2x from both sides:
2x - 6 - 2x > 5x - 14 - 2x

Simplifying further, we get:
-6 > 3x - 14

Now, add 14 to both sides of the inequality:
-6 + 14 > 3x - 14 + 14

Simplifying, we have:
8 > 3x

Divide both sides of the inequality by 3:
8/3 > 3x/3

Simplifying further, we get:
8/3 > x

So, the solution for the inequality is x < 8/3.

1. To represent this solution on a number line, draw a horizontal line with an open circle at 8/3 and an arrow pointing to the left side, indicating that x can take any value less than 8/3.

2. There is no need to graph this solution on a coordinate plane since it is a one-dimensional line.

I hope this explanation helps you solve and graph these equations and inequalities!