Solve equations, simplify expressions, calculate area, and find equivalent fractions
Check the final answer first, then review the worked steps.
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. $\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$.