Solve equations, simplify expressions, calculate area, and find equivalent fractions
Check the final answer first, then review the worked steps.
Problem
Solve equations, simplify expressions, calculate area, and find equivalent fractions
Answer
1. x = 4; 2. y = 7; 3. 9a - 12; 4. 60; 5. 3/4
Step-by-step solution
- Solve 2x + 3 = 11: Subtract 3 from both sides to get $2x = 8$. Divide by 2 to find $x = 4$.
- Solve 3y - 5 = 16: Add 5 to both sides to get $3y = 21$. Divide by 3 to find $y = 7$.
- Simplify 4(2a - 3) + a: Distribute the 4 into the parentheses: $8a - 12 + a$. Combine the like terms ($8a + a$): $9a - 12$.
- Calculate the area of a rectangle: The area of a rectangle is given by $Area = length \times width$. Substituting the given values: $12 \text{ cm} \times 5 \text{ cm} = 60 \text{ cm}^2$.
- Find the equivalent fraction for 6/8: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2. $\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$.