Solve the inequality then graph the solution set on real number line.
(2/5x)>7
2(x+7)-4>5(x-3)
the easy one first:
2(x+7)-4>5(x-3)
2x + 14 - 4 > 5x - 15
-3x > -25
x < 25/3
for the 1st, I don't know why you put brackets around the left side, since it serves no purpose
did you mean 2/(5x) > 7
or
(2/5)x > 7
I will assume the last case:
mulitply both sides by 5
2x > 35
x > 35/2
To solve the inequality (2/5x) > 7, we can follow these steps:
Step 1: Multiply both sides of the inequality by 5 to eliminate the fraction:
5 * (2/5x) > 5 * 7
2x > 35
Step 2: Divide both sides of the inequality by 2 to isolate the variable:
(2x) / 2 > 35 / 2
x > 35/2
Now we have solved the inequality.
To graph the solution set on the real number line, we need to represent all the values of x that make the inequality true.
The solution x > 35/2 indicates that x can take any value greater than 35/2.
On the number line, we can mark a point at 35/2, and draw an arrow from that point to the right, indicating that x is greater than 35/2. Since there are infinitely many numbers greater than 35/2, the arrow should extend indefinitely to the right.
The graph would look like this:
------------------------------->
35/2
Now let's move on to the second inequality, 2(x+7) - 4 > 5(x-3).
Step 1: Distribute the 2 and 5 on their respective terms:
2x + 14 - 4 > 5x - 15
Simplify:
2x + 10 > 5x - 15
Step 2: Move the x terms to one side and the constant terms to the other side:
2x - 5x > -15 - 10
-3x > -25
Step 3: Divide both sides of the inequality by -3. Remember that when dividing or multiplying by a negative number, the inequality sign should be flipped:
(-3x) / -3 < (-25) / -3
x < 25/3
The solution to the inequality is x < 25/3.
To represent this solution on the real number line, we mark a point at 25/3 and draw an arrow to the left, indicating that x is less than 25/3. Since there are infinitely many numbers less than 25/3, the arrow should extend indefinitely to the left.
The graph would look like this:
<-------------------------------
25/3
I hope this explanation helps you understand how to solve inequalities and graph their solutions on the real number line. If you have any further questions, feel free to ask!