Math Problem Statement
Solution
I see the mathematical exercises from the uploaded image. Let’s break down and explain the solutions for both exercises.
Exercise 5:
You are asked to combine like terms and solve the equations, giving the solution set.
a)
- Combine all terms with :
- Combine constants: Equation simplifies to:
- Subtract 8 from both sides:
- Divide by 10: Solution set:
b)
- Combine all terms with :
- Combine constants: Equation simplifies to:
- Subtract 26 from both sides:
- Divide by 11: Solution set:
Exercise 6:
You are tasked with solving equations by expanding the brackets and finding .
a)
- Distribute :
- Subtract 15 from both sides:
- Divide by 3:
b)
- Distribute :
- Subtract 24 from both sides:
- Divide by 6:
c)
- Distribute :
- Add 15 to both sides:
- Divide by 3:
d)
- Distribute :
- Add 20 to both sides:
- Divide by 4:
Would you like any of these steps detailed further? Here are five questions you might want to explore:
- How do we solve equations with fractions or decimals?
- Can you explain the distributive property further?
- What happens when there are variables on both sides of the equation?
- How do we solve inequalities using similar steps?
- Can we graph the solutions to these equations?
Tip: Always check your solution by substituting back into the original equation to ensure it satisfies it!
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Math Problem Analysis
Mathematical Concepts
Algebra
Equation Solving
Distributive Property
Formulas
ax + b = c
a(b + c) = ab + ac
Theorems
-
Suitable Grade Level
Grades 7-8
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