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Solve 2x+3=11, 3y-5=16, simplify 4(2a-3)+a, area of 12x5 rectangle, simplify 6/8

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

Problem

Solve 2x+3=11, 3y-5=16, simplify 4(2a-3)+a, area of 12x5 rectangle, simplify 6/8

Answer

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

Step-by-step solution

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

Worksheet preview

Four practice prompts on the first page, with answers and short solutions on the second page.

  1. 1 Solve for x: 2x + 3 = 11.
  2. 2 Solve for x: 2x + 3 = 15.
  3. 3 Solve for x: 2x + 3 = 5.
  4. 4 Solve for x: 2x + 3 = 21.