Let's solve the equation \( 6 = \frac{3}{4}(10x + 16) \).

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 4 to eliminate the denominator:

\[
4 \times 6 = 4 \times \frac{3}{4}(10x + 16)
\]

\[
24 = 3(10x + 16)
\]

### Step 2: Distribute the 3 on the right-hand side
\[
24 = 3 \times 10x + 3 \times 16
\]
\[
24 = 30x + 48
\]

### Step 3: Isolate the variable term
Subtract 48 from both sides to move the constant to the left side:
\[
24 - 48 = 30x
\]
\[
-24 = 30x
\]

### Step 4: Solve for \( x \)
Divide both sides by 30:
\[
x = \frac{-24}{30}
\]

Simplify the fraction:
\[
x = \frac{-4}{5}
\]

### Final Answer:
\[
x = -\frac{4}{5}
\]

Would you like more details or have any questions?

Here are 5 related questions to extend your understanding:
1. What if the coefficient of \( x \) were different?
2. How do you solve equations with two variables?
3. Can you solve an equation like \( 6 = \frac{2}{3}(8x + 12) \)?
4. How would you graph \( y = \frac{3}{4}(10x + 16) \)?
5. What are the steps for solving quadratic equations?

**Tip:** Always simplify fractions where possible to make solving easier.

Discover how to solve the linear equation 6 = (3/4)(10x + 16) step by step. This solution explores algebraic techniques like eliminating fractions, applying the distributive property, and simplifying fractions. Ideal for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation