Negative three times the sum of a number and one is less than or equal to the difference of 5 times the number and 9.Graph the solutions.
-3(x+1) <= 5x-9
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plot y = -3(x+1) , y = 5x-9
You want the region where the blue line is below the red line: x >= 3/4
To solve this equation and graph the solutions, we need to follow a few steps:
Step 1: Assign a variable to the unknown quantity in the problem.
Let's use the variable 'x' to represent the number mentioned in the problem.
Step 2: Translate the problem into an equation.
The problem states that negative three times the sum of a number and one is less than or equal to the difference of 5 times the number and 9. We can express this in mathematical terms as:
-3(x + 1) ≤ 5x - 9
Step 3: Solve the equation for x.
First, distribute the negative three to (x + 1):
-3x - 3 ≤ 5x - 9
Next, isolate the variable terms on one side of the inequality by adding 3x and subtracting 5x from both sides:
-3 - 9 ≤ 5x + 3x
Combine like terms:
-12 ≤ 8x
Then, divide both sides of the inequality by 8 to solve for x:
-12/8 ≤ x
Simplifying further, we have:
-3/2 ≤ x
Step 4: Graph the solutions.
To graph the solutions, we need to plot all the values of x that satisfy the inequality -3/2 ≤ x.
The graph will include all x-values greater than or equal to -3/2. This means we will have a shaded region to the right of -3/2 on the number line. We can represent this graphically as follows:
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◄──╯
The shaded region to the right of -3/2 represents all the values of x that satisfy the inequality.