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!