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Solve equations, simplify expressions, find area, and equivalent fractions

Check the final answer first, then review the worked steps.

Problem

Solve equations, simplify expressions, find area, and equivalent fractions

Answer

1. x = 4; 2. y = 7; 3. 9a - 12; 4. 60; 5. 3/4

Step-by-step solution

  1. Solve 2x + 3 = 11: Subtract 3 from both sides to get $2x = 8$. Divide by 2 to find $x = 4$.
  1. Find the value of y for 3y - 5 = 16: Add 5 to both sides to get $3y = 21$. Divide by 3 to find $y = 7$.
  1. Simplify 4(2a - 3) + a: Distribute the 4 to get $8a - 12 + a$. Combine like terms ($8a + a$) to get $9a - 12$.
  1. Find the area of a rectangle: The area of a rectangle is calculated as $length \times width$. Given $12 \text{ cm}$ and $5 \text{ cm}$, the area is $12 \times 5 = 60 \text{ cm}^2$.
  1. Find the equivalent fraction to 6/8: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2. $\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$.