Which Inequality Is Equivalent To?

There are many inequalities that are equivalent to each other. For example, the following inequalities are all equivalent to each other:

-x < y -x^2 < y^2 -|x| < |y|

In general, any two inequalities that have the same solution set are considered equivalent. So, if we can solve one inequality and find that its solution set is the same as the solution set of another inequality, then we can say that the two inequalities are equivalent.

One way to show that two inequalities are equivalent is to use algebra to manipulate one inequality into the other. For example, suppose we want to show that the following two inequalities are equivalent:

-x < y -x^2 < y^2

We can start by squaring both sides of the first inequality:

(-x)^2 < y^2

Since (-x)^2 = x^2, this is the same as:

x^2 < y^2

Thus, we have shown that the two inequalities are equivalent.

Another way to show that two inequalities are equivalent is to graph both inequalities on a number line and see that their solution sets are the same. For example, consider the following two inequalities:

-x < y |x| < |y|

We can graph both of these inequalities on a number line:

-x < y -y < x < y

|x| < |y|

-y < x < y

From looking at the graphs, we can see that the solution sets of both inequalities are the same. Therefore, the two inequalities are equivalent.

There are many other ways to show that two inequalities are equivalent. In general, any time two inequalities have the same solution set, we can say that the inequalities are equivalent.

On a similar theme: Which System of Inequalities Is Shown in the Graph?

There are a few different ways to approach this question. One way to think about it is to consider what would make the two sides of the equation equal. In other words, what would you need to add to or subtract from the left side of the equation (x+4) to make it equal to the right side of the equation (9)?

In this case, you would subtract 4 from each side of the equation. This would give you the equation x>5. So, the inequality equivalent to the equation x+4>9 is x>5.

Another way to think about this question is to consider what the inequality is saying. The inequality is saying that x+4 is greater than 9. So, if we wanted to write this as an equation, we would write it as x+4=9.

We can also approach this question by solving for x. To do this, we would subtract 4 from each side of the equation. This would give us the equation x=5. So, the inequality equivalent to the equation x+4>9 is x=5.

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There are two types of inequality, strict and non-strict. The strict inequality is represented by the symbol "<" which means "less than". The non-strict inequality is represented by the symbol "≤" which means "less than or equal to".

The equation x-6<4 is a strict inequality. This means that x is less than 4. The inequality equivalent to this equation is x≤3. This means that x is less than or equal to 3.

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There are a few different ways to answer this question. One way to think about it is to consider the various ways that two times a number plus one could be greater than seven.

For example, if x=3, then 2(3)+1=7, so 3 is not a solution. However, if x=4, then 2(4)+1=9, which is greater than 7. Therefore, we can say that the inequality equivalent to the equation 2x+1>7 is x>3.

Another way to think about it is to consider the left side of the equation as a function and the right side as a constant. In this case, the function is f(x)=2x+1 and the constant is 7. We are looking for the values of x that make the function greater than the constant.

For f(x)=2x+1, we can see that the y-intercept is 1 and the slope is 2. Therefore, the line representing this function will be above the y-intercept (1) when x is positive and below the y-intercept when x is negative. The y-intercept is also the point where the line crosses the y-axis (7 in this case), so we can say that the function is above the y-axis when x is positive and below the y-axis when x is negative.

Therefore, the solutions to the inequality 2x+1>7 are all the values of x that are positive (and therefore above the y-axis).

Here's an interesting read: Logarithmic Equation

There are a few different ways to approach this question. First, we could solve for x in the inequality to find out what values of x would make the inequality true. We would do this by adding 3x to both sides of the inequality and then subtracting 2 from both sides. This would give us the equation x<6. So, the inequality -3x+2<4 is equivalent to the inequality x<6.

Another way to approach this question is to think about what the inequality means. The inequality is saying that -3x+2 is less than 4. So, we could also say that -3x is less than 2. This is the same as saying that x is greater than -2/3. So, the inequality -3x+2-2/3.

Related reading: Which Values of X Satisfy the Inequality?

In order to answer this question, we must first understand what is meant by the term "inequality equivalent." An inequality equivalent is an inequality that has the same solution as the original inequality. In other words, if we were to solve both inequalities, we would get the same answer.

Now that we know what we are looking for, let's take a look at the equation given to us. We can see that the equation is asking us to find what x is less than 2. In order to solve this, we would subtract 5 from both sides of the inequality. This would give us the following:

x<-3

We can see that the solution to this inequality is all values of x that are less than -3. So, the inequality equivalent to the equation x+5<2 is x<-3.

A unique perspective: 3 5

The answer to this question is quite simple. The inequality is equivalent to the equation -x+4>6 because when you solve for x, you get -4>2. This means that the only possible value for x is -4, and since -4 is not greater than 2, the inequality is not true.

There are a few different ways to interpret this question, so we will explore a few different approaches.

One way to think about this is to consider the graph of the equation. We can see that the left hand side of the inequality is a line with a slope of 3 and a y-intercept of -1. The right hand side of the inequality is a horizontal line at y=10. So the inequality is equivalent to asking where the line x=3x-1 falls below the line y=10. This will happen when x is less than 7.

We could also approach this algebraically. We can solve the inequality for x to get x<7. So the inequality is asking us to find all values of x that are less than 7.

Another way to think about this is to consider the meaning of the inequality. It is saying that 3x is less than 11, or that x is less than (11/3). So it is asking us to find all values of x that are less than (11/3).

In all of these cases, the answer is the same: the inequality is equivalent to x<7.

For your interest: Inequality Mc011 1 Jpg

There are a few different ways to answer this question. One way to think about it is to consider the two sides of the inequality as two separate equations and then solve for x. Doing this, we would have:

-4x + 7 -2/-4 x > 1/2

This means that the inequality is equivalent to x being greater than 1/2. Another way to think about it is to consider what the inequality means in terms of the values of x that would make it true. In other words, we are looking for all values of x such that -4x + 7 < 5. This can be rewritten as:

7 - 4x < 5 3 < 4x

This means that the inequality is equivalent to x being greater than 3/4.

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The inequality equivalent to the equation 5x-3>4 is 5x>7. To solve this inequality, we need to find the values of x that make the inequality true. We can do this by graphing the equation on a number line.

We start by graphing the 5x-3>4 inequality. We know that the> symbol means that the line will be slanted to the right, so we will start at the point 4 and draw a line going up and to the right. Our line will intersect the x-axis at the point 7, since 7 is the only value of x that makes the inequality true.

Now that we have graphed the inequality, we can see that the values of x that make the inequality true are all the values of x that are greater than 7. So, the inequality 5x>7 is equivalent to the equation 5x-3>4.