Question

If 8x + 5x + 2x + 4x = 114, the 5x + 3 =

• A. 12
• B. 25
• C. 33
• D. 47
• E. 86

Hint:

Always read the question carefully to the very end. A common mistake is to solve for 'x' and choose that as the answer, but the question often asks for the value of an expression containing 'x'.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a two-part algebra problem. First, you must solve a linear equation to find the value of the variable 'x'. Second, you must substitute this value of 'x' into a separate expression to find its value.
Step 2: Key Formula or Approach:
1. Solve the equation for 'x' by combining like terms and isolating 'x'.
2. Substitute the found value of 'x' into the expression \( 5x + 3 \).
Step 3: Detailed Explanation:
Part 1: Solve for x.
The given equation is: \[ 8x + 5x + 2x + 4x = 114 \] Combine all the terms with 'x' on the left side: \[ (8 + 5 + 2 + 4)x = 114 \] \[ 19x = 114 \] Now, solve for 'x' by dividing both sides by 19: \[ x = \frac{114}{19} \] To calculate this, you can recognize that 19 is close to 20. \( 20 \times 6 = 120 \). Let's check \( 19 \times 6 \): \( (20 - 1) \times 6 = 120 - 6 = 114 \). \[ x = 6 \] Part 2: Evaluate the expression.
The question asks for the value of \( 5x + 3 \).
Substitute the value \( x = 6 \) into this expression: \[ 5(6) + 3 \] \[ 30 + 3 = 33 \] Step 4: Final Answer:
The value of the expression \( 5x + 3 \) is 33. The correct option is (C).