What is the solution set of 2x−3=5 and 5x+3>−12?
To solve the equation 2x − 3 = 5, we can begin by isolating the variable.
Adding 3 to both sides, we have:
2x = 5 + 3
2x = 8
Finally, dividing both sides by 2 yields:
x = 4
Now, let's solve the inequality 5x + 3 > -12.
Subtracting 3 from both sides, we have:
5x > -12 - 3
5x > -15
Next, dividing both sides by 5, we obtain:
x > -15/5
x > -3
Therefore, the solution set consists of all values greater than -3.
Let's solve the equations step by step:
Equation 1: 2x - 3 = 5
Step 1: Add 3 to both sides of the equation to isolate the variable term:
2x - 3 + 3 = 5 + 3
Simplifying, we get:
2x = 8
Step 2: Divide both sides of the equation by 2 to solve for x:
2x/2 = 8/2
Simplifying further, we have:
x = 4
So, the solution to the equation 2x - 3 = 5 is x = 4.
Equation 2: 5x + 3 > -12
Step 1: Subtract 3 from both sides of the equation to isolate the variable term:
5x + 3 - 3 > -12 - 3
Simplifying, we get:
5x > -15
Step 2: Divide both sides of the equation by 5 to solve for x:
5x/5 > -15/5
Simplifying further, we have:
x > -3
So, the solution to the inequality 5x + 3 > -12 is x > -3.
Therefore, the solution set for the system of equations 2x - 3 = 5 and 5x + 3 > -12 is x = 4 and x > -3.
To find the solution set of the given equations, we will solve each equation individually and then combine the results.
Let's start with the first equation: 2x - 3 = 5.
To isolate the variable, we can add 3 to both sides of the equation:
2x - 3 + 3 = 5 + 3
Simplifying, we get:
2x = 8
Now, divide both sides of the equation by 2 to solve for x:
2x/2 = 8/2
It simplifies to:
x = 4
So, the solution to the first equation is x = 4.
Now let's move on to the second inequality: 5x + 3 > -12.
To solve an inequality, we want to isolate the variable x on one side of the inequality sign.
First, subtract 3 from both sides of the inequality:
5x + 3 - 3 > -12 - 3
This simplifies to:
5x > -15
Now, divide both sides of the inequality by 5 to solve for x:
5x/5 > -15/5
It simplifies to:
x > -3
So, the solution to the second inequality is x > -3.
Now that we have the solutions to both equations, we can combine them to find the solution set.
From the first equation, we found that x = 4.
From the second inequality, we found that x > -3.
So, the solution set consists of all values of x that satisfy both conditions: x = 4 and x > -3.
Therefore, the solution set is {x | x = 4, x > -3}.