Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.
<h3>What are inequalities?</h3>
Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given Inequalities can be solved as,
5 - x > 7
-x > 7 - 5
-x > 2
x < -2
2x + 3 ≥ 13
2x ≥ 10
x ≥ 5
As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.
This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.
Learn more about Inequality:
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Answer:
2 ≤ x
Step-by-step explanation:
Answer:
0,2 0r 2/2
Step-by-step explanation:
Answer:
x = 3, 5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients/Degrees
- Standard Form: ax² + bx + c = 0
- Multiple Roots
- Factoring
- Completing the Square: -b/(2a)
Step-by-step explanation:
<u>Step 1: Define</u>
x² - 8x + 15 = 0
<u>Step 2: Solve for </u><em><u>x</u></em>
- [Subtraction Property of Equality] Subtract 15 on both sides: x² - 8x = -15
- Complete the Square [Addition Property of Equality]: x² - 8x + 16 = -15 + 16
- [Complete the Square] Simplify: (x - 4)² = 1
- [Equality Property] Square root both sides: x - 4 = ±1
- [Addition Property of Equality] Add 4 on both sides: x = 4 ± 1
- Evaluate: x = 3, 5
Let the four numbers be A,B,C,D in ascending order.
The key is in conditions 2 & 3.
B-C=-4, and B+C=0
therefore B=-2, C=2 by solving the two previous equations.
Given that the product of the two greatest numbers is 6, we have C*D=6, or
D=6/C=6/2=3
Now since the sum of all the four numbers is -6, we have
A+B+C+D=-6
A-2+2+3=-6
A=-6+2-2-3=-9
Check: we were told smallest divided by greatest = A/D=-9/3=-3 ok.
So the numbers are
A=-9, B=-2, C=2, D=3.
