Solve the inequality and graph the solution on the line provided.
minus, 8, plus, 6, x, is greater than, minus, 56
−8+6x>
−56
To solve the inequality, we will isolate the variable on one side of the inequality symbol.
Starting with the inequality −8 + 6x > −56:
First, we add 8 to both sides:
−8 + 8 + 6x > −56 + 8
6x > −48
Next, we divide both sides by 6 (since the coefficient of x is 6 and we want to isolate x):
(6x)/6 > (-48)/6
x > -8
The solution to the inequality is x > -8.
Now let's graph the solution on the number line:
We start with an open circle on -8 to indicate that x is not equal to -8, but greater than -8. Then we draw an arrow to the right to represent all the possible values of x greater than -8.
Here is the graph of the solution:
<------------------(=============-]------------------>
-8
To solve the inequality -8 + 6x > -56, we need to isolate the variable "x" on one side of the inequality symbol.
First, let's simplify the left side of the inequality:
-8 + 6x > -56
Combine like terms:
6x - 8 > -56
Next, we'll add 8 to both sides of the inequality to isolate the term with "x":
6x - 8 + 8 > -56 + 8
This simplifies to:
6x > -48
Finally, we divide both sides of the inequality by 6 to solve for "x":
(6x)/6 > (-48)/6
This gives us:
x > -8
The solution to the inequality is x > -8.
Now, let's graph the solution on a number line:
-8 -------------------------------------->
Since the solution is x > -8, we use an open circle at -8 to indicate that -8 itself is not included in the solution. Then, we draw an arrow to the right to represent all the numbers greater than -8, which are part of the solution.
To solve the inequality −8+6x > −56, follow these steps:
Step 1: Start by isolating the variable term (6x) on one side of the inequality. To do this, add 8 to both sides of the inequality:
−8 + 8 + 6x > −56 + 8
This simplifies to:
6x > −48
Step 2: Next, divide both sides of the inequality by the coefficient of the variable (6) to solve for x:
(6x) / 6 > (−48) / 6
Simplifying yields:
x > -8
So, the solution to the inequality is x > -8.
To graph the solution on a number line:
1. Draw a number line and place a closed circle or dot on the number -8 as it is not included in the solution.
2. Extend an arrow to the right of the dot to represent all the values greater than -8.
- The dot indicates that -8 is not included in the solution, and the arrow represents the range of values greater than -8.
The graphed solution on the line would appear as follows:
<---○--------------->
-8 (all values to the right)