Math Problem Statement
solve these
Solution
Let's solve each of the given equations step by step.
4.
- Distribute the constants on both sides:
- Move the terms involving to one side:
- Solve for :
5.
- Distribute the constants:
- Subtract from both sides: This is a contradiction, so there is no solution.
6.
- Distribute :
- Move the terms involving to one side:
- Solve for :
7.
- Distribute on both sides:
- Combine like terms:
- Move the terms involving to one side:
- Solve for :
8.
- Distribute on both sides:
- Move the terms involving to one side:
- Solve for :
9.
- Distribute on both sides:
- The equation simplifies to: This is an identity, so any value of will satisfy the equation.
10.
- Distribute the fractions:
- Move the terms involving to one side:
- Solve for :
11. Three consecutive integers are , , and . Four times the sum of the least and greatest integers is 12 less than three times the least integer. What is the least integer?
- Express the sum of the least and greatest integers:
- Four times the sum:
- Set up the equation based on the problem:
- Move the terms involving to one side:
- Solve for :
Would you like a detailed explanation for any of these solutions or have any questions?
Related Questions:
- How do you solve systems of linear equations?
- What are the different types of equations encountered in algebra?
- Can you solve quadratic equations by factoring?
- What is the method of substitution in solving linear equations?
- How do you interpret the solution of a linear equation graphically?
Tip:
Always verify your solutions by substituting them back into the original equations to ensure they satisfy all given conditions.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Distributive property
Solving equations
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9