Solve the inequality. Graph the solution set and write it in interval notation.
4x - 3 > 3x - 7
Write the answer in interval notation.
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To solve the inequality, we need to isolate the variable x.
Starting with the given inequality: 4x - 3 > 3x - 7
We can subtract 3x from both sides of the inequality: 4x - 3 - 3x > 3x - 7 - 3x
Simplifying: x - 3 > -7
Next, we can add 3 to both sides of the inequality: x - 3 + 3 > -7 + 3
Simplifying: x > -4
So the solution to the inequality is x > -4.
To graph the solution set, we draw a number line and shade everything to the right of -4.
On the number line, we mark a solid circle at -4 (since the inequality is "greater than" and not "greater than or equal to"), and shade everything to the right of it.
In interval notation, the solution set is (-4, ∞).
To solve the inequality 4x - 3 > 3x - 7, we will isolate the x variable.
First, let's subtract 3x from both sides:
4x - 3x - 3 > 3x - 3x - 7
Simplifying:
x - 3 > -7
Next, let's add 3 to both sides:
x - 3 + 3 > -7 + 3
Simplifying:
x > -4
Now, to graph the solution set, we represent all values of x that are greater than -4 on a number line:
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The inequality x > -4 represents all values to the right of -4, but not including -4.
Finally, let's write the solution set in interval notation based on the graph:
The solution set is (-4, ∞), meaning x is greater than -4, but not including -4.
To solve the inequality 4x - 3 > 3x - 7, we need to isolate the variable x.
First, let's subtract 3x from both sides of the inequality:
4x - 3 - 3x > 3x - 7 - 3x
This simplifies to:
x - 3 > -7
Next, let's add 3 to both sides of the inequality:
x - 3 + 3 > -7 + 3
This simplifies to:
x > -4
The solution to the inequality is x > -4.
To graph the solution set, we plot a number line and mark the point -4 with an open circle. Since the inequality is not inclusive of -4, we leave an open circle on the number line at -4. Then, we shade to the right of -4 to represent the values greater than -4.
The graph of the solution set on the number line would look like this:
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To write the answer in interval notation, we represent the numbers greater than -4 using inequality symbols. In this case, the solution set can be written as:
(-4, ∞)
This indicates that x is greater than -4 and there is no upper bound, since we use the infinity symbol (∞). The parentheses indicate that -4 is not included in the solution set.