How do you solve this inequality?
2x over 4 minus 5x+1 over 3 is greater than 3
multiply each term by 12 to get
6x - 20x - 4 > 36
It should be easy from here on, let me know what you got
I assume that you mean
(2x/4) - (5x+1)/3 > 3
x/2 - (5x+1)/3 > 3
Multiply both sides by 6.
3x - 10x -2 > 18
Add 2 to both sides and combine x terms.
-7x > 20
Divide both sides by -7. Multiplying by a negative number requires that the direction of > be reversed.
x < 20/7
(IF I interpreted your original inequality correctly)
2x/4_(5x+1)/3>3
Multiply both sides by LCM that is
(2x/4)12_[(5x+4)/3>3
Answer equals to 6x_20x_4>36
6x_20x>36+4
_14x>40
Divide both sides by_14 that is
_14x/_14>40/_14
Answer equals to x<_20/7
x<_20/7
I'm sorry, I made a mistake in my previous response. Let's solve it correctly this time.
We have the inequality:
2x/4 - (5x + 1)/3 > 3
We want to get rid of the fractions, so multiply both sides of the inequality by 12 (the least common multiple of 4 and 3):
12 * (2x/4) - 12 * ((5x + 1)/3) > 12 * 3
Simplifying, we get:
6x - 4(5x + 1) > 36
Distribute the -4:
6x - 20x - 4 > 36
Combine like terms:
-14x - 4 > 36
Add 4 to both sides:
-14x > 40
Now, divide both sides by -14. Remember that dividing by a negative number flips the inequality sign:
x < 40/-14
Simplifying, we get:
x < -20/7
So, the solution to the inequality is x < -20/7.
To solve the inequality:
1. Simplify the equation on both sides, if possible.
2. Get rid of any fractions by multiplying both sides by the least common denominator (LCD) of all the denominators.
3. Combine like terms and simplify, if necessary.
4. Move all the variable terms to one side of the inequality and the constant terms to the other side.
5. Isolate the variable term by dividing both sides by the coefficient of the variable.
6. Determine if the inequality sign should be flipped based on whether you divided by a negative number or not.
7. Write the solution using interval notation or as a graph on the number line.
Now, let's solve the given inequality step by step:
1. Simplify the equation:
2x/4 - (5x + 1)/3 > 3
2. Find the LCD:
The denominators are 4 and 3. The LCD is 4 * 3 = 12.
3. Get rid of the fractions by multiplying both sides by 12:
12 * (2x/4) - 12 * ((5x + 1)/3) > 12 * 3
(24x)/4 - (12(5x + 1))/3 > 36
4. Simplify the expression:
6x - 4(5x + 1) > 36
6x - 20x - 4 > 36
-14x - 4 > 36
5. Move constant terms to the other side:
-14x > 36 + 4
-14x > 40
6. Divide both sides by -14 (remembering to flip the inequality sign):
x < -40/14
x < -20/7
7. Write the solution:
When x is less than -20/7, the inequality is true. So the solution can be represented as:
x ∈ (-∞, -20/7) or in interval notation: (-∞, -20/7)
That's how you solve the given inequality.