name the definition of these terms

Question

Solution set
expression
inequality
equation
inverse operations

Answer 1

Sure! Here are the definitions of the terms you've requested:

1. Solution Set: The solution set is the collection of all possible values that satisfy a given equation or inequality. It represents the set of solutions that make the equation or inequality true.

2. Expression: An expression is a mathematical phrase that can include numbers, variables, operators (such as +, −, ×, and ÷), and function symbols. Unlike an equation, an expression does not contain an equality sign. It represents a value but does not assert that two expressions are equal.

3. Inequality: An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Common inequality symbols include > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

4. Equation: An equation is a mathematical statement that asserts the equality of two expressions. It contains an equals sign (=) and indicates that the expressions on both sides have the same value. It can be true for some values of the variable(s) and false for others.

5. Inverse Operations: Inverse operations are pairs of mathematical operations that reverse the effect of each other. For example, addition and subtraction are inverse operations; if you add a number and then subtract the same number, you return to the original value. Similarly, multiplication and division are also inverse operations.

If you have further queries or need more details on any of these concepts, feel free to ask!

Answer 2

which value of m will make the equation true -(5m+6)=2(3m+8)
these are the possible answers for m
-10
-2
11
All real numbers

Answer 3

To find the value of \( m \) that makes the equation \( -(5m + 6) = 2(3m + 8) \) true, let's solve the equation step by step.

1. Start with the original equation: \[ -(5m + 6) = 2(3m + 8) \]

2. Distribute the negative sign on the left side: \[ -5m - 6 = 2(3m + 8) \]

3. Now distribute the 2 on the right side: \[ -5m - 6 = 6m + 16 \]

4. Next, we'll collect all the \( m \) terms on one side and the constant terms on the other side. First, add \( 5m \) to both sides: \[ -6 = 6m + 5m + 16 \] Which simplifies to: \[ -6 = 11m + 16 \]

5. Now, subtract 16 from both sides: \[ -6 - 16 = 11m \] This simplifies to: \[ -22 = 11m \]

6. Finally, divide both sides by 11: \[ m = -2 \]

Thus, the value of \( m \) that makes the equation true is \(-2\).

The correct answer from your choices is: -2.

Answer 4

which values of x will make the equation x^2=16 true? select all that apply
-4
0
4
8
-8

Answer 5

To determine which values of \( x \) will make the equation \( x^2 = 16 \) true, we can solve for \( x \) by taking the square root of both sides.

1. Start with the equation: \[ x^2 = 16 \]

2. Taking the square root of both sides gives us: \[ x = \pm 4 \]

This indicates that \( x \) can be either \( 4 \) or \( -4 \).

Now, we can check the provided values:

• -4: \( (-4)^2 = 16 \) (True)
• 0: \( (0)^2 = 0 \) (Not true)
• 4: \( (4)^2 = 16 \) (True)
• 8: \( (8)^2 = 64 \) (Not true)
• -8: \( (-8)^2 = 64 \) (Not true)

The values of \( x \) that will make the equation \( x^2 = 16 \) true are -4 and 4.

So the correct selections are: -4 and 4.

Answer 6

which of the following solutions are written in set notation
{6}
(x)
56
{x:x<3}

Answer 7

In set notation, solutions are typically given in the form of sets, which are denoted by curly braces {} and describe the elements within the set or certain properties of those elements.

Let's analyze the options you provided:

1. {6}: This is written in set notation. It represents a set containing the single element 6.

2. (x): This is not written in set notation. It appears to be a notation for a variable or a function, not a set.

3. 56: This is simply a number and is not in set notation.

4. {x: x < 3}: This is written in set notation. It represents the set of all \( x \) such that \( x \) is less than 3.

Thus, the solutions written in set notation are:

• {6}
• {x: x < 3}

Answer 8

solve 3(x-8)+4x≥-3

Answer 9

To solve the inequality \( 3(x - 8) + 4x \geq -3 \), we can follow these steps:

1. Distribute \( 3 \) in the expression: \[ 3x - 24 + 4x \geq -3 \]

2. Combine like terms: \[ (3x + 4x) - 24 \geq -3 \] \[ 7x - 24 \geq -3 \]

3. Add \( 24 \) to both sides to isolate the term with \( x \): \[ 7x \geq -3 + 24 \] \[ 7x \geq 21 \]

4. Divide both sides by \( 7 \): \[ x \geq 3 \]

Thus, the solution to the inequality \( 3(x - 8) + 4x \geq -3 \) is:

\[ \boxed{x \geq 3} \]

This means \( x \) can take any value greater than or equal to \( 3 \).

Answer 10

solve 5x+6≤21

Answer 11

To solve the inequality \( 5x + 6 \leq 21 \), follow these steps:

1. Subtract \( 6 \) from both sides to isolate the term with \( x \): \[ 5x \leq 21 - 6 \] \[ 5x \leq 15 \]

2. Divide both sides by \( 5 \): \[ x \leq 3 \]

Thus, the solution to the inequality \( 5x + 6 \leq 21 \) is:

\[ \boxed{x \leq 3} \]

This means \( x \) can take any value less than or equal to \( 3 \).